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1
In a bowl, mix the yeast, a pinch of the sugar and 1/2 cup of the water and let stand until foamy.
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2
Stir in the egg, salt and the remaining sugar and 1 1/2 cups of water.
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3
Add 5 cups of the flour and stir to form a soft, sticky dough.
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4
Stir in the stick of softened butter.
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5
Add the remaining 1 cup of flour and stir.
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6
When the dough becomes too stiff, scrape it out onto a work surface and knead until smooth; add a few tablespoons of flour if necessary to keep the dough from sticking.
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7
Transfer the dough to a lightly buttered bowl, cover with plastic wrap and let rise in a draft-free place until doubled in bulk, 1 hour.
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8
Punch down the dough and knead 2 or 3 times; cover and let rest for 15 minutes.
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9
On a very lightly floured surface, roll out the dough 3/8 inch thick.
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10
Using a 2 3/4-inch round cutter dipped in flour, stamp out 24 rounds as close together as possible; if necessary, reroll and cut out some of the scraps.
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11
Reserve the scraps.
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12
Melt the remaining 10 tablespoons of butter in a small saucepan; set aside 2 tablespoons.
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13
Dip both sides of each round in the remaining butter, letting any excess drip into the pan.
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14
Fold the rounds in half and set, folded side down, in a 9-by-13-inch glass baking dish.
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15
Toss the reserved scraps with any leftover butter and arrange them in a single layer in an 8-inch square baking dish.
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16
Cover both dishes with plastic wrap and let the rolls rise in a draft-free spot until nearly doubled in bulk, about 1 hour.
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17
Preheat the oven to 425.
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18
Remove the plastic and bake the rolls for 30 minutes, or until golden, shifting the pans halfway through baking.
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19
Remove the rolls from the oven and brush the tops with the reserved 2 tablespoons of butter.
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20
Let cool for 10 minutes.
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21
Invert the rolls onto a wire rack, set a platter on top and invert again.
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22
Serve warm or at room temperature.
