Preheat oven to 450°F. Mix flour, cornmeal, baking powder, caraway seed and salt in large bowl. Stir in cheese. Cut in butter with pastry blender or 2 knives until mixture resembles coarse crumbs. Stirring with fork, add enough milk until mixture leaves sides of bowl and forms a soft, moist dough.
Knead dough lightly on floured surface until no longer sticky. Roll or press dough to 1/2-inch thickness. Cut with floured 2-inch round cutter. Place on ungreased baking sheet.
Bake 8 to 10 minutes or until light golden brown. Serve warm.