With a sharp knife, score each chestnut 1/4-inch deep all around. Arrange them in one layer in a baking pan and roast for 20 minutes, or until shells have just opened. Peel off both layers of skin with a knife while the nuts are still hot. In a large saucepan of boiling, salted water, cook the Brussels sprouts for 12 to 15 minutes, or until tender. Drain and refresh with cold water. Then thinly slice the cooled Brussels sprouts.
In a large skillet set over moderately high heat, melt the butter, add the shallots and cook, stirring, 2 minutes. Add the chestnuts, Brussels sprouts, herbs, and salt and pepper, and saute for 2 to 3 minutes, or until heated through.