Combine the warm water and the yeast in a large bowel. Let the mixture stand until yeast is foamy, about 5 minutes.
Stir in butter, sugar, eggs and salt. Beat in flour, 1 cup at a time, until dough is too stiff to mix (some flour may not be needed). Cover and refrigerate 2 hours or up to 4 days.
Grease a 13-x9-inch baking pan. Turn the chilled dough out onto a lightly floured board. Divide dough into 24 equal-size pieces. Roll each piece into a smooth round ball; place balls in even rows in the prepared pan. Cover and let dough balls rise until doubled in volume, about 1 hour.
Preheat oven to 375 F. Bake until rolls are golden brown, 15-20 minutes. Brush warm rolls with melted butter, if desired. break rolls apart to serve.