In a large bowl, whisk together 1½ cups flour with the sugar, salt, and yeast.
In a small saucepan, heat 1 cup milk and ½ cup butter until about 115°; pour the milk mixture into the flour mixture and blend on low speed until incorporated.
Add the eggs and blend again, and then beat the dough on medium speed for 3 minutes.
Gradually stir in additional flour (about 2 cups should do it) until the dough pulls away from the sides of the bowl.
Turn out the dough on a floured work surface and knead for about 4 to 5 minutes, adding small amounts of flour as needed to keep the dough from sticking.
Place the dough in a large greased bowl, turning the dough so the entire surface is greased.
Cover and let rise until double, about an hour.
Punch down the dough and then turn out onto a lightly floured work surface.
Divide the dough into 24 pieces.
Roll each piece into a 15-inch rope.
Grease cookie sheets (you will probably need 3 total) and, working directly on the prepared cookie sheet, loosely coil each rope into a circle, tucking the ends underneath.
Cover and let the rolls rise until double, about 20 to 30 minutes.
Meanwhile, preheat the oven to 350°.