Step 1: Whisk water, oil, and sugar together in a 4-cup liquid measuring cup until sugar dissolves.
Step 2: In a stand mixer fitted with dough hook, mix flour, potato flakes, yeast and 11/2 teaspoons salt on slow speed unit combined. Add water mixture in steady stream and mix until dough comes together, about 1 minute. Increase speed to medium low and knead until dough is smooth and comes away from bowl, about 6 minutes.
Step 3: Turn dough onto a lightly floured counter and knead briefly to form a smooth ball. Transfer dough to a bowl slightly coated with oil and turn to coat. Cover with plastic wrap and place in a warm place until doubled in size, about 45 minutes.
Step 4: On lightly floured counter, gently press down dough. Divide into quarters and cut each quarter into three pieces. Form each piece into a ball by pinching and pulling edges under so that top is smooth. Cup each ball with palm and move in circular motion to shape into a smooth taught ball.
Step 5: Transfer to baking sheet lined with parchment and cover loosely with plastic that you have first sprayed with cooking spray. Put in a warm area to rise, about 20 minutes.
Step 6: Remove plastic wrap and brush rolls with egg and sprinkle with salt. Bake until rolls are just beginning to brown and outside is set, about 15 minutes.
Step 7: Can be refrigerated after shaped into rolls for up to 24 hours. Bake directly from refrigerator.
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