Preheat oven: Preheat your oven to 375°F (190°C).

Cook potatoes: Boil the potatoes until tender, then drain and mash them.

Sauté onion: In a skillet, melt the butter over medium heat. Add the onion and cook until softened, about 5 minutes.

Combine ingredients: In a large bowl, combine the mashed potatoes, cooked onion, eggs, milk, salt, and pepper. Stir until well combined.

Bake: Pour the mixture into a greased baking dish. Sprinkle with cheddar cheese. Bake for 30-35 minutes, or until the casserole is set and golden brown.