In a large bowl, combine the warm water and yeast. Let the mixture stand until the yeast is foamy, about 5 minutes. If it does not become foamy, your yeast is probably old and not active- it's best to throw it out and start again.
With a wooden spoon, stir in the butter, sugar, eggs and salt. Beat in the flour, 1 cup at a time, until the dough is too stiff to mix (all of the flour may not be needed). The dough should no longer be sticky. Place the round ball of dough into a new bowl that has been sprayed with nonstick spray. Cover with plastic wrap and refrigerate 2 hours or up to 4 days.
Grease a 13x9-inch baking pan. Turn the chilled dough out onto a lightly floured board. Divide the dough into 24 equal-size pieces. Roll each piece into a smooth round ball; place balls in even rows (4 rows by 6 rows) in the prepared pan. Cover with a dish towel and let the dough balls rise until doubled in volume, about 1 hour (or so). You can leave them to rise longer if you need to.
Preheat the oven to 375° F. Bake until the rolls are golden brown and cooked through, 15-20 minutes. If they are browning too quickly on top, tent foil over the rolls until finished baking. Brush warm rolls with melted butter, if desired. Break rolls apart to serve.
Notes
*nutritional info. does not include extra melted butter brushed on top.
*In this recipe, don't use quick-rising dry yeast.
*Before adding the yeast mixture, use an instant-read thermometer to check the temperature of the water (it's important that it's in the temperature range indicated)
*These rolls may be baked early in the day and re-warmed when ready to serve.