Preheat the oven to 375 degrees F (190 degrees C). Grease the bottom and sides of 12 muffin cups.
Melt butter in a saucepan over medium heat. Add onion and garlic; saute until tender, about 5 minutes. Add half-and-half and Parmesan, Mexican, Cheddar, and American cheeses. Stir until all cheeses have melted, about 2 minutes. Season sauce with nutmeg, thyme, pepper, and seafood seasoning.
Lay 1 potato slice in the bottom of each muffin cup. Top with a spoonful of the cheese sauce. Layer on another potato slice and spoonful of sauce. Repeat until potato slices are used up or cups are full, ending with cheese sauce on top.
Bake in the preheated oven until hot and bubbly, about 40 minutes. Cover with foil for the last 10 minutes if top is browning too much. Let stand for 5 minutes before removing.
Substitute milk for the half-and-half if desired.
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