In a small mixing bowl combine warm water and yeast.
Let stand 5 minutes or until bubbly.
Meanwhile in a large mixing bowl combine
2 3/4 cups flour, the 1/2 cup Parmesan cheese,
basil, sugar, and salt.
Add yeast mixture.
Stir until combined.
Turn dough out onto a lightly floured surface.
Knead in enough remaining flour to make
a moderately stiff dough that is smooth and
elastic (6 to 8 minutes total).
Shape into a ball.
Place dough in a lightly greased bowl,
turning once to greased surface.
Cover; let rise in a warm place until double
(about 1 hour). Punch dough down.
Turn dough out onto a lightly floured surface.
Divide in half. Cover and let rest 10 minutes.
Divide each half of dough into twelve portions
(24 portions total).
Gently pull each portion of dough into a ball,
tucking edges beneath.
Arrange balls, smooth side up,
in 24 lightly greased 1 3/4" muffin cups.
Cover and let rise in a warm place
until nearly double in size (about 30 minutes).
Preheat oven to 400F.
Brush tops with milk and sprinkle with
the 2 tablespoons of Parmesan cheese.
Bake for 12-15 minutes or
until tops are golden brown.
Remove rolls from pan. Serve warm.