Preheat oven to 375º F. In the microwave, melt butter in a small glass measuring cup with a pour spout. Pour a bit of butter into each well of a standard-sized 12-cup muffin tin. Brush the butter up the sides and around the top edge of each muffin cup (if your pan is not non-stick, you may want to use a little extra butter to prevent sticking).
Whisk eggs, milk, all but 2 tablespoons of the cheese, salt, and paprika in a mixing bowl with a pour spout (a bowl with a pour spout is not strictly necessary, but it makes it much easier and tidier and to add batter to the muffin cups). Whisk until well combined. Add the flour and whisk until blended.
Pour batter into the prepared muffin cups, filling each cup about half full. Sprinkle the remaining cheese over the batter in each cup.
Bake popovers in preheated oven for 30 minutes without opening the oven.
Remove popovers from the oven and prick each one with a fork or skewer to let the steam escape. Serve warm.