In a large bowl mixing bowl, combine 2 cups flour, sugar, yeast and salt. Add water and oil; beat on medium speed for 2 minutes. Add the egg and vinegar; beat on high for 2 mins. Stir in cheese ans enough remaining flour to form a stiff dough.
Turn onto a floured surface; Knead until dough is smooth and no longer sticky; about 2 mins.
Roll dough to about 1/2 inch thickness. cut with a 3- inch round cutter. Roll scraps if desired. Coat baking sheets with nonstick spray and sprinkle with 2 tablespoons cornmeal. Cover and let rise until doubled, about 1 hour.
Heat an ungreased griddle or electric skillet to 325*. Cook muffins for 20 to 25 minutes or until golden brown, turning every 5 minutes Remove to wire racks to cool. Split with a fork and toast if desired.