Combine milk, 3 tablespoons butter, sugar, and salt in a large mixing bowl; let cool to lukewarm (105° to 115°). Add 2 cups flour, mixing well.
Dissolve yeast in lukewarm water. Let stand 5 minutes. Add dissolved yeast and egg to milk mixture, mixing well. Add remaining flour, mixing well.
Turn dough out onto a lightly floured surface. Knead 1 minute or until dough is smooth and elastic. Place dough in a greased bowl. Melt remaining butter; brush surface of dough lightly with butter. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk. Punch dough down; cover and let rest 10 minutes.
Turn dough out onto a surface that has been sprinkled with cornmeal. Roll dough to 1/4- inch thickness; cut with a 3- inch biscuit cutter. Sprinkle cornmeal over tops of muffins. Place muffins on ungreased baking sheets. Cover and repeat rising procedure 45 minutes or until doubled in bulk.
Place muffins on an ungreased griddle or skillet. Cook over low heat 12 minutes or until browned; turn and cook an additional 12 minutes to brown other side. Split muffins, and toast, if desired.