Preheat the oven to 400⁰F. In a heavy 9x13 roasting pan or casserole, toss the Brussels sprouts and shallots. In a cup, stir the olive oil, honey and champagne vinegar and drizzle over the Brussels sprout mixture. Add the salt and pepper and toss to coat.
Roast, uncovered, at 400⁰F for 20 minutes, stir, and roast for 20 minutes more. The Brussels sprouts will be browned and slightly shrunken.
Serve warm or at room temperature. These keep wall in the refrigerator for up to four days.