Heat oven to 400 F (200 C). Butter or spray a baking dish or ovenproof skillet.

Layer slices of potatoes and butternut squash along the bottom of the dish (I overlapped the rows a little bit). Sprinkle a little salt and pepper over the layer, then top with the onions and garlic. Add another layer of potatoes and squash and add another sprinkle of salt and pepper. Set aside.

Make the cheese sauce. In a medium saucepan, melt the butter. Add the flour and mix until fully incorporated, and cook for 2-3 minutes to get rid of the raw flour taste. Slowly add the milk while stirring to prevent lumps. Add the salt, pepper, and thyme and stir. Add all of the shredded cheese and stir until melted fully. Taste and see if it needs more salt (remember, potatoes can handle A LOT of salt!).

Pour the cheese sauce evenly over the potato/squash layers and top with the parmesan. Cover the dish tightly with aluminum foil and bake for 60-75 minutes until the potatoes are fork-tender. Remove the foil and broil for 2-5 minutes (keep a close eye on it!) until the cheese is browned to your taste.