Preheat the oven to 375°.
Bake the potatoes until soft when tested with a knife, about 1 hour.
Leave the oven on.
While still warm but cool enough to handle, cut the top third off each potato horizontally.
Scoop out the potato in the bottom section and put into a large bowl.
Save the shells.
Mash the potatoes with the butter and milk.
Mix in the cooked corn, cheese, salt, and pepper.
Stuff the potato shells equally with the mashed potato mixture.
Bake the stuffed potatoes until piping hot all the way through and lightly browned on top, 20 to 25 minutes.