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Boil the cubed potatoes in a large pot of salted water until tender, about 10 minutes. Drain and return to the pot.
Mash the potatoes with melted butter, warmed milk, 1 teaspoon salt, and 1/2 teaspoon black pepper until smooth. Set aside.
In a large skillet over medium-high heat, heat the olive oil. Add the chopped onion and diced carrots, cooking until softened, about 4 minutes.
Add the ground beef to the skillet and cook until browned, breaking it up with a spoon, about 5 minutes.
Stir in the tomato paste, beef broth, frozen peas, 1 teaspoon salt, and 1/2 teaspoon black pepper. Simmer for 5 minutes until the sauce thickens.
Preheat the broiler. Spread the beef mixture in an even layer in a 9x13 inch baking dish. Top with the mashed potatoes, spreading to cover the beef completely.
Place under the broiler until the top is golden brown, about 3 minutes. Serve immediately.

Boil the cubed potatoes in a large pot of salted water until tender, about 10 minutes. Drain and return to the pot.
Mash the potatoes with melted butter, warmed milk, 1 teaspoon salt, and 1/2 teaspoon black pepper until smooth. Set aside.
In a large skillet over medium-high heat, heat the olive oil. Add the chopped onion and diced carrots, cooking until softened, about 4 minutes.
Add the ground beef to the skillet and cook until browned, breaking it up with a spoon, about 5 minutes.
Stir in the tomato paste, beef broth, frozen peas, 1 teaspoon salt, and 1/2 teaspoon black pepper. Simmer for 5 minutes until the sauce thickens.
Preheat the broiler. Spread the beef mixture in an even layer in a 9x13 inch baking dish. Top with the mashed potatoes, spreading to cover the beef completely.
Place under the broiler until the top is golden brown, about 3 minutes. Serve immediately.