In a large mixing bowl, combine the warm water, active dry yeast, and a small pinch of the sugar.

Let the yeast mixture sit for 5–10 minutes, until foamy.

Add the remaining sugar, softened butter, warm milk, eggs, and salt to the yeast mixture.

Stir until mostly combined; the butter may remain slightly lumpy.

Add the flour 1 cup at a time, stirring after each addition. Start with 5 1/2 cups and add more only if the dough is too sticky to handle.

Turn the dough onto a lightly floured surface and knead for 6–8 minutes, until smooth, elastic, and soft. If using a stand mixer, knead with the dough hook on low speed for 4–5 minutes.

Place the dough in a greased bowl and turn once so the top is lightly coated.

Cover and let rise in a warm place for about 1 hour, or until doubled in size.

Punch the dough down gently, cover the bowl tightly, and refrigerate for at least 4 hours or overnight.

When ready to bake, remove the dough from the refrigerator and punch it down again.

Divide the dough into 24 pieces and shape each piece into a smooth ball.

Place the rolls in greased baking pans, leaving a little space between them.

Cover and let rise in a warm place for 45–60 minutes, or until puffy.

Preheat the oven to 375°F.

Bake for 15–18 minutes, or until the tops are golden brown.

Brush the warm rolls with melted butter as soon as they come out of the oven.