Melt butter in a saucepan over medium-high heat.

Add flour and cook, browning slightly to create a thick roux.

Stir in sour cream, green chilies, salt, and pepper. Let the sauce thicken to the consistency of thick gravy.

If needed, thin the sauce by adding milk, 1 tablespoon at a time.

Remove the sauce from heat and stir in most of the grated Monterey Jack cheese, reserving some for topping.

Slice unpeeled potatoes into 1/4-inch thick slices.

Place a layer of potato slices in a small casserole dish.

Pour half of the cheese sauce over the potato layer.

Add another layer of potato slices and pour the remaining cheese sauce over it.

Bake in a preheated oven at 350°F (175°C) for 45 minutes to 1 hour.

Top with the remaining grated cheese and bake for an additional 15 minutes, or until golden brown and bubbly.