Trim the bottoms from the brussels sprouts and remove any dry leaves from the outside. Cut them in half through the stem if they are very large.
Place the brussels sprouts in the slow cooker. Add the butter, mustard, maple syrup, broth or water, and salt and pepper, as well as they cayenne if using. Stir well to coat the Brussels sprouts with the sauce.
Cover and cook on high for 2 hours, or low for 4 hours. Stir to redistribute the glaze, and serve hot.