Preheat an oven to 450 degrees F (230 degrees C). Prick potatoes several times with a fork and place onto a baking sheet.
Bake in the preheated oven until potatoes are easily pierced with a fork, 50 minutes to 1 hour. Remove from the oven and set aside until cool enough to handle.
Preheat a nonstick waffle iron for medium heat according to manufacturer's instructions.
Scoop potato flesh into a large bowl with butter, milk, salt, onion powder, garlic powder, and pepper; mash until creamy. Stir in Cheddar cheese until evenly distributed. Discard potato skins or set aside for another use.
Place some potato mixture in the preheated waffle iron; do not cover the entire surface. Close the iron and the batter will spread out. Cook until brown and crispy, about 5 minutes. Repeat with remaining batter.