A touch of cream transforms this dish into a sumptuous side that exposes the luxurious character of this often homely vegetable.
Bring butter, salt, pepper, and 1 cup water to a boil over high heat in a deep 12-inch heavy skillet, then add Brussels sprouts and simmer, partially covered, stirring occasionally, until crisp-tender, 6 to 8 minutes.
Remove lid and boil over moderately high heat until water is evaporated and sprouts are lightly browned, 3 to 4 minutes. Add cream and remaining 1/4 cup water and bring to a boil, stirring. Add chestnuts, then reduce heat and simmer, stirring occasionally, until heated through, about 2 minutes.