Mom's Two-Crust Potato Pie

Place the potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Mash the potatoes with 1/4 cup butter, 1/4 cup milk, salt, and black pepper to make medium-stiff mashed potatoes; stir in the American cheese. Preheat oven to 375 degrees F (190 degrees C). Fit a crust into a 9-inch pie dish, and fill with the potato mixture. Place the top crust on the pie, roll the edges together and crimp with a fork to seal. Stir the melted butter and 2 teaspoons of milk together in a small bowl, and brush the mixture all over the pie crust. Cut several vent holes in the top of the crust. Bake the pie in the preheated oven until the crust is golden brown, about 45 minutes; if the edges are getting too brown, wrap them in aluminum foil.