Preheat an oven to 350 degrees F (175 degrees C). Butter a large baking dish.
Wash and peel the potatoes so that only some of the peel remains on the potatoes; cut into 1/8 inch slices. Put the potatoes in the prepared dish.
Melt the butter in a large pot over medium-high heat. Cook the onion and garlic in the melted butter until soft and translucent, 7 to 10 minutes; stir in the broccoli soup, celery soup, milk, salt, pepper, and about half of the Cheddar cheese; cook until the cheese has melted. Pour the mixture over the potatoes; top with the remaining Cheddar cheese. Cover with aluminum foil or lid.
Bake in the preheated oven for 45 minutes. Remove the cover and cook until the cheese begins to brown, about 10 minutes more.
