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Add all ingredients to Bread Machine and select 'Dough' function.
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When done, punch down dough (do not knead) then halve. Roll half of dough on a lightly floured surface with lightly floured hands into a 12 inch long log (keep remaining half covered in plastic.).
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Cut log into 6 equal pieces, then cut each piece into thirds. Roll each piece into a 1 inch ball by cupping your hand and pushing dough against work surface as you roll in circular motion. Put 3 balls side by side in each of 6 muffin cups.
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Make more rolls with the remaining dough in the same manner. Cover rolls with a kitchen towel (not terry cloth) and let rise in a draft-free place at warm room temperature until dough is about 1 inch above the rim of the muffin cups, 1 to 1-1/2 hours.
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Preheat oven to 375 degrees with rack in the middle.
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(If desired, whisk together 1 egg and 1 tbsp water and brush on top of rolls).
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Bake until golden brown, about 20 minutes. Transfer to a rack and cool at least 20 minutes.