Combine milk and cornmeal in a heavy saucepan; cook and stir for for 6-8 minutes over medium heat until thickened and bubbly. Remove from heat and add butter, salt, and all but about a teaspoon of the sugar. Cool to lukewarm. If it is hotter than 120°, it will kill your yeast!
While the cornmeal mixture is cooling, dissolve the yeast in the warm water with the reserved teaspoon of sugar. Let it sit for 5-10 minutes or until it is foamy or bubbly.
Add the yeast mixture, cooled cornmeal mixture, eggs, and 1 1/2-2 cups of the flour to a large mixing bowl. Beat at medium speed with an electric hand mixer until smooth.
Gradually add enough flour to make a soft and slightly sticky dough.
Cover and let rise in a warm place until doubled, usually 60-90 minutes.
Punch the dough down to remove air bubbles. Form the dough into 24 round balls and place on a cookie sheet that has been sprayed with cooking spray. Cover with a lid or plastic wrap. Let rise till doubled (usually about 30-40 minutes).
When the rolls are almost doubled, preheat your oven to 350°. Bake on a lower oven rack at 350° for about 25-30 minutes, or till golden brown. If desired, brush with butter while still hot.