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Step 1
Proof the yeast: In the bowl of a stand mixer, combine the water, the yeast, and 1 teaspoon of the sugar. Set aside for about 5 minutes, or until the mixture looks bubbly. If the mixture doesn't start to bubble, then your yeast has likely expired and it's best to start over with new yeast.
Step 2
Mix the dough: Add the remaining sugar, mashed potatoes, milk, butter, eggs, rosemary, and salt to the bowl with the yeast mixture and stir with a spatula until smooth. Add 4 1/2 cups of the flour and mix until you form a shaggy dough.
Step 3
Knead the dough: With a dough hook attachment (or on the counter, if kneading by hand) knead on medium-low for 5 to 7 minutes until the dough is smooth, forms a ball around the dough hook, and pulls away from the sides of the bowl (it's fine if the dough sticks to the bottom of the bowl). If the dough is still sticking to the sides after few minutes of kneading, add in a little more flour 2 tablespoons at a time.
Step 4
Let the dough rise: Place the dough in a lightly greased bowl, cover with plastic wrap, and place somewhere warm for about 1 hour, or until the dough doubles in size.
Step 5
Shape the dough into rolls: Line a 13x9-inch baking pan with parchment paper and lightly grease. Turn the dough the out onto lightly floured surface and cut into 16 to 20 equal pieces. Roll the dough into small balls, and place seam side down in the baking dish.
Step 6
Cover and let the rolls rise until puffed and nearly doubled in size, about 1 hour. About 15 minutes before the rolls are ready, heat the oven to 350F.
Step 7
Bake for the rolls for 20 to 25 minutes, or until the rolls are golden brown on top and register 200F on the inside when tested with an instant-read thermometer.
Step 8
Brush the rolls with honey butter: In a small dish, mix together 1/4 cup room temperature butter and 2 tablespoons honey until smooth. Brush tops of baked rolls with mixture, then sprinkle with salt. Allow to cool slightly before serving.