Asolutely delicious, and kind of like Brussels sprouts au gratin. They make a tempting fall and winter side dish. and I would eat them as a vegetarian main dish any time.
Preheat the oven to 375 F. If the Brussels sprouts are large, you may want to cut the halves into quarters.
Heat the butter in a large ovenproof skillet over medium heat, then sauté the shallots for 1 minute until they begin to soften. Add the Brussels sprouts and sauté for 5 minutes until the outsides start to soften and brown just a bit. Pour over the half-and-half or cream, which will quickly start to simmer. Add the cheddar and the Parmesan and stir until the cheeses have started to melt.
Transfer the pan to the oven and bake for 15 minutes until the whole thing is bubbly and the top is browned (a last minute under the broiler is a-ok for a little extra browning – just watch it carefully).
Notes
Looking to add these to Thanksgiving or another cooking-intense day? You can even make them up ahead until the baking time, set them aside for a couple of hours, then sprinkle on the cheese and bake them right before serving. No last-minute fiddling on the stovetop!