Preheat the oven to 350ºF. Then, in a medium saucepan, melt some butter and sautee the onion until softened.
Add arrowroot and stir until a smooth paste forms.
Add milk and cook on medium, stirring frequently, until a thick white sauce is formed (it will seem TOO thick; this is okay).
Pour the sauce into an 8 x 8 baking dish and add the shrimp, salt, pepper, and cheeses before stirring to combine.
Bake for 25 - 30 minutes. Serve immediately.