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Prepare the pasta dough: In a large mixing bowl, whisk together the semolina flour, all-purpose flour, and 1/2 teaspoon salt. Create a well in the center of the flour mixture. Crack the 4 large eggs into the well and add 1 tablespoon of olive oil.
Using a fork, gently whisk the eggs and olive oil, gradually incorporating flour from the sides of the well until a shaggy dough forms. Turn the dough out onto a clean, lightly floured surface and knead for 10 to 15 minutes, until the dough is smooth, elastic, and no longer sticky. It should spring back when lightly pressed.
Form the dough into a ball, wrap it tightly in plastic wrap, and let it rest at room temperature for at least 30 minutes. This allows the gluten to relax, making the dough easier to roll.
While the dough rests, prepare the puttanesca sauce: Heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium heat. Add the minced garlic and mashed anchovy fillets. Cook for 2 to 3 minutes, stirring constantly, until the garlic is fragrant and the anchovies have dissolved into the oil.
Stir in the 28 ounces of crushed tomatoes, 1/2 cup of Kalamata olives, 2 tablespoons of drained capers, and 1/2 teaspoon of red pepper flakes. Bring the sauce to a gentle simmer, then reduce the heat to low, cover, and let it cook for 20 minutes, stirring occasionally.
After the dough has rested, unwrap it and cut it into four equal portions. Working with one portion at a time, keep the remaining dough covered to prevent it from drying out. Lightly flour your work surface and a pasta machine (or rolling pin).
Roll the dough through a pasta machine, starting at the widest setting and gradually decreasing the thickness, one notch at a time, until the dough sheet is about 1/16 inch thick (or to the second-to-last setting on most machines). If using a rolling pin, roll it out as thinly as possible.
Lay the thin pasta sheet on a lightly floured surface. Using a fluted pasta wheel or sharp knife, cut the dough into 1 1/2 inch by 1 1/2 inch squares. To form garganelli, take each square and place it diagonally on a garganelli board (or gnocchi board, or a fork with a wooden skewer). Roll the square tightly from one corner to the opposite, pressing gently to create the ridged tube shape. Place the formed garganelli on a lightly floured baking sheet.
Bring a large pot of salted water to a rolling boil. While the water boils, stir the chopped fresh parsley and fresh basil into the puttanesca sauce. Season the sauce with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper, adjusting to taste.
Carefully add the handmade garganelli to the boiling water. Cook for 3 to 5 minutes, or until the pasta floats to the surface and is al dente. Since it's fresh pasta, it will cook quickly.
Using a slotted spoon, transfer the cooked garganelli directly into the puttanesca sauce. Toss gently to coat the pasta evenly with the sauce. If the sauce seems too thick, add a tablespoon or two of the pasta cooking water to loosen it.
Serve immediately, garnished with extra fresh basil or parsley if desired.

Prepare the pasta dough: In a large mixing bowl, whisk together the semolina flour, all-purpose flour, and 1/2 teaspoon salt. Create a well in the center of the flour mixture. Crack the 4 large eggs into the well and add 1 tablespoon of olive oil.
Using a fork, gently whisk the eggs and olive oil, gradually incorporating flour from the sides of the well until a shaggy dough forms. Turn the dough out onto a clean, lightly floured surface and knead for 10 to 15 minutes, until the dough is smooth, elastic, and no longer sticky. It should spring back when lightly pressed.
Form the dough into a ball, wrap it tightly in plastic wrap, and let it rest at room temperature for at least 30 minutes. This allows the gluten to relax, making the dough easier to roll.
While the dough rests, prepare the puttanesca sauce: Heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium heat. Add the minced garlic and mashed anchovy fillets. Cook for 2 to 3 minutes, stirring constantly, until the garlic is fragrant and the anchovies have dissolved into the oil.
Stir in the 28 ounces of crushed tomatoes, 1/2 cup of Kalamata olives, 2 tablespoons of drained capers, and 1/2 teaspoon of red pepper flakes. Bring the sauce to a gentle simmer, then reduce the heat to low, cover, and let it cook for 20 minutes, stirring occasionally.
After the dough has rested, unwrap it and cut it into four equal portions. Working with one portion at a time, keep the remaining dough covered to prevent it from drying out. Lightly flour your work surface and a pasta machine (or rolling pin).
Roll the dough through a pasta machine, starting at the widest setting and gradually decreasing the thickness, one notch at a time, until the dough sheet is about 1/16 inch thick (or to the second-to-last setting on most machines). If using a rolling pin, roll it out as thinly as possible.
Lay the thin pasta sheet on a lightly floured surface. Using a fluted pasta wheel or sharp knife, cut the dough into 1 1/2 inch by 1 1/2 inch squares. To form garganelli, take each square and place it diagonally on a garganelli board (or gnocchi board, or a fork with a wooden skewer). Roll the square tightly from one corner to the opposite, pressing gently to create the ridged tube shape. Place the formed garganelli on a lightly floured baking sheet.
Bring a large pot of salted water to a rolling boil. While the water boils, stir the chopped fresh parsley and fresh basil into the puttanesca sauce. Season the sauce with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper, adjusting to taste.
Carefully add the handmade garganelli to the boiling water. Cook for 3 to 5 minutes, or until the pasta floats to the surface and is al dente. Since it's fresh pasta, it will cook quickly.
Using a slotted spoon, transfer the cooked garganelli directly into the puttanesca sauce. Toss gently to coat the pasta evenly with the sauce. If the sauce seems too thick, add a tablespoon or two of the pasta cooking water to loosen it.
Serve immediately, garnished with extra fresh basil or parsley if desired.