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).