Put all of the ingredients except for the potatoes and cheese in a saucepan and heat over medium-low heat. Simmer for 10 minutes.
Layer the potatoes in a casserole dish, seasoning with salt and pepper between layers. Pour the milk over the top and cover with foil. Bake for 45 minutes and remove from oven.
Top with the cheese and bake for 15-20 more minutes, until cheese is browned and bubbly.