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In the bowl of a stand mixer, combine the all-purpose flour, granulated sugar, active dry yeast, and salt. Mix briefly to combine. Add the warm water, beaten egg, softened unsalted butter, and cooled mashed potatoes to the dry ingredients.

Attach the dough hook to the stand mixer and mix on low speed until the ingredients are just combined. Increase speed to medium-low and knead for 8-10 minutes, or until the dough is smooth, elastic, and passes the 'window pane' test (a small piece of dough can be stretched thin enough to see light through it without tearing). The dough will be soft and slightly sticky.

Lightly grease a large bowl with cooking spray or a little oil. Transfer the dough to the bowl, turning once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1 1/2 hours, or until doubled in size.

Gently punch down the risen dough to release the air. Turn the dough out onto a lightly floured surface. Divide the dough into 6 equal pieces. Shape each piece into a smooth, round roll. Arrange the rolls in a lightly greased 8x8 inch baking pan or on a parchment-lined baking sheet, leaving a little space between them.

Cover the rolls loosely with plastic wrap or a clean kitchen towel and let them rise again in a warm place for 30-45 minutes, or until noticeably puffy and nearly doubled in size.

While the rolls are rising for the second time, preheat your oven to 375°F.

Bake the rolls in the preheated oven for 15-20 minutes, or until golden brown on top and cooked through. If rolls are browning too quickly, you can loosely tent them with aluminum foil.

Once baked, remove the rolls from the oven. If desired, brush the tops with melted butter for extra shine and flavor. Let the rolls cool slightly in the pan before serving warm.

To freeze the dough: After shaping (Step 4), place the shaped rolls on a parchment-lined baking sheet and flash-freeze until solid (about 2-3 hours). Transfer the frozen rolls to a freezer-safe bag or container and store for up to 1 month. When ready to bake, thaw the rolls overnight in the refrigerator, then let them come to room temperature and rise (Step 5) before baking as directed.

In the bowl of a stand mixer, combine the all-purpose flour, granulated sugar, active dry yeast, and salt. Mix briefly to combine. Add the warm water, beaten egg, softened unsalted butter, and cooled mashed potatoes to the dry ingredients.

Attach the dough hook to the stand mixer and mix on low speed until the ingredients are just combined. Increase speed to medium-low and knead for 8-10 minutes, or until the dough is smooth, elastic, and passes the 'window pane' test (a small piece of dough can be stretched thin enough to see light through it without tearing). The dough will be soft and slightly sticky.

Lightly grease a large bowl with cooking spray or a little oil. Transfer the dough to the bowl, turning once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1 1/2 hours, or until doubled in size.

Gently punch down the risen dough to release the air. Turn the dough out onto a lightly floured surface. Divide the dough into 6 equal pieces. Shape each piece into a smooth, round roll. Arrange the rolls in a lightly greased 8x8 inch baking pan or on a parchment-lined baking sheet, leaving a little space between them.

Cover the rolls loosely with plastic wrap or a clean kitchen towel and let them rise again in a warm place for 30-45 minutes, or until noticeably puffy and nearly doubled in size.

While the rolls are rising for the second time, preheat your oven to 375°F.

Bake the rolls in the preheated oven for 15-20 minutes, or until golden brown on top and cooked through. If rolls are browning too quickly, you can loosely tent them with aluminum foil.

Once baked, remove the rolls from the oven. If desired, brush the tops with melted butter for extra shine and flavor. Let the rolls cool slightly in the pan before serving warm.

To freeze the dough: After shaping (Step 4), place the shaped rolls on a parchment-lined baking sheet and flash-freeze until solid (about 2-3 hours). Transfer the frozen rolls to a freezer-safe bag or container and store for up to 1 month. When ready to bake, thaw the rolls overnight in the refrigerator, then let them come to room temperature and rise (Step 5) before baking as directed.
