1. In a food processor fitted with a steel blade, process 3-1/4 cups flour, the yeast, sugar, and salt just to blend. With on/off pulsing, cut in butter finely, until it almost disappears.

2. In a separate bowl, mix together mashed potato, milk, and egg. With processor motor running, quickly add potato mixture to yeast mixture. Process until mixture comes away from the side of the bowl.

3. Process 30 seconds to knead dough. If dough is sticky, add more flour and process 15 to 30 seconds longer. Dough should feel tacky, smooth, elastic, and warm but not hot.

4. Remove dough from processor and shape into a ball. Place ball in an oiled bowl, turn to cover it with oil, and cover bowl with plastic wrap or a damp towel. Let dough rise until doubled in bulk.

5. Punch dough down. Let rest 5 minutes. Divide dough into 24 pieces (approximately 1-1/4 ounces each). Shape each piece into a ball, tucking the edges under to draw the surface of the dough tight. Arrange the dough in 2 round cake or pie pans. Cover loosely with plastic wrap or a damp towel and let rise until doubled in bulk.

6. Preheat oven to 375 degrees F. Brush tops with melted butter. Bake until golden brown (20 to 30 minutes). Remove from pan to cool on a wire rack. Brush tops again with melted butter.

Makes 2 dozen rolls.