These rolls are best served warm but can be made one day ahead and stored in an airtight container at room temperature.
Combine milk with butter and salt in a saucepan and bring to a boil, stirring until butter melts. Gradually whisk in cornmeal. Reduce heat to medium and cook, stirring frequently, until thickened, 2 to 3 minutes. Transfer to a bowl and let cool completely.
In a large bowl, whisk yeast and sugar into 1/3 cup warm water (110 degrees). Let stand until foamy, then stir in cornmeal mixture. Lightly beat 2 eggs; stir into yeast-and-cornmeal mixture. Stir in 3 1/2 cups flour until dough is tacky but not sticky. (If dough is sticky, stir in more flour.) Transfer to a work surface dusted with flour. Knead with floured hands, dusting more flour onto hands and surface as needed, until dough is elastic and springs back when pressed with a finger, about 5 minutes.
Transfer dough to a large bowl brushed with butter. Cover and let rise in a warm spot until doubled in volume, about 1 hour. The dough can be made up to this point and left torise up to 12 hours in the refrigerator; remove from refrigerator 1 hour before proceeding.
Punch down dough. Form into a ball and place on a clean, undusted work surface. Quarter dough, then divide each quarter into 4 pieces. Form each piece into a ball and space evenly on two rimmed baking sheets that are generously dusted with cornmeal (8 per sheet). Loosely cover and let rise until doubled in volume, about 45 minutes.
Preheat oven to 375 degrees with racks in upper and lower thirds. Beat remaining egg. Brush tops of rolls with egg, then slash a 1/4-inch-deep X in tops. Lightly dust with cornmeal and sprinkle with flaky salt.
Bake, rotating sheets halfway through, until rolls are puffed, golden, and hollow-sounding when tapped on bottoms, 18 to 20 minutes. Transfer to a basket lined with a clean towel and cover to keep warm until ready to serve.