Preheat your oven to 350 degrees F and generously butter a large baking dish.
Wash and peel the red potatoes, leaving some of the peel on for that rustic feel. Slice the potatoes into 1/8-inch slices and place them in the prepared baking dish.
In a large pot, melt the butter over medium-high heat. Add the chopped onion and garlic, cooking until they become soft and translucent (around 7 to 10 minutes).
Stir in the condensed cream of broccoli soup, condensed cream of celery soup, milk, salt, pepper, and about half of the shredded Cheddar cheese. Allow the mixture to cook until the cheese has melted and all the flavors are well combined.
Pour this creamy mixture over the sliced potatoes in the baking dish, ensuring an even distribution.
Sprinkle the remaining shredded Cheddar cheese on top of the potatoes.
Cover the baking dish with aluminum foil or a lid and bake in the preheated oven for 45 minutes.
Remove the cover and continue baking for an additional 10 minutes, or until the cheese on top turns a beautiful golden brown.