1. Whisk milk and eggs, then whisk in flour, salt, pepper, and sage. Stir in 1/2 cup cheese. Let stand 1 hour.
2. Preheat oven to 450° at least 30 minutes before baking. Divide butter among 12 popover cups. Put pans in oven 2 minutes to melt butter. Set a rimmed baking sheet on rack beneath to catch any dripping butter as popovers rise.
3. Stir batter and ladle into cups. Bake 10 minutes. Without opening oven, reduce heat to 375° and bake until popovers are puffed and golden, about 15 minutes more. Top each with a large pinch of remaining cheese and return to oven to melt cheese, 5 minutes.
4. Free popovers from pan by running a thin metal spatula around edge; lift from bottom.
Note: Nutritional analysis is per popover.