Preheat oven to 375.
Bring a large pot of water to boil and add the Brussels sprouts. Cook for 5 minutes, or until nearly tender. Drain the sprouts and run cold water over them. Pat them dry and set aside.
Meanwhile, heat a large skillet over medium heat and add the butter. Add the shallot and garlic and cook until shallots are translucent, about 3 - 5 minutes. Whisk in the flour and cook for 1 minute. Whisk in the milk slowly. Continue to whisk until sauce thickens.
Remove the skillet from the heat and add the cheese, stirring until melted. Taste and season with salt and pepper. Add the brussel sprouts to the pan and stir to coat with the cheese sauce.
Transfer the mixture to a large baking dish and sprinkle with the parmesan cheese and panko. Bake in the oven for 25 to 30 minutes, or untilt the sauce is bubbling and the cheese on top is melted and golden brown. Serve and enjoy