Whisk milk and eggs, then whisk in flour, salt, pepper, and sage. Stir in 1/2 cup cheese. Let stand 1 hour.
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.
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.
Free popovers from pan by running a thin metal spatula around edge; lift from bottom.
Note: Nutritional analysis is per popover.