Melt 1/4 cup plus 2 tablespoons butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add half-and-half; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in salt and pepper. Set aside.
Sauté chestnuts and mushrooms in 2 tablespoons butter in a large skillet for 2 minutes. Add Brussels sprouts; sauté an additional 2 minutes.
Place vegetable mixture in a shallow 3-quart baking dish. Pour reserved sauce over vegetable mixture; sprinkle with cheese. Bake at 300° for 30 minutes.