Cut any large Brussels sprouts in half. Place Brussels sprouts in a 3 1/2- or 4-quart slow cooker. Sprinkle sprouts with salt and pepper. Combine in a bowl the chicken broth and mustard. Pour over sprouts in cooker.
Cover and cook on low-heat setting for 4 to 4 1/2 hours or on high-heat setting for 2 1/2 to 3 hours.
With a slotted spoon, remove Brussels sprouts to a serving dish. Cover sprouts with foil to keep warm.
If using low-heat setting, turn to high-heat setting. Combine in a small bowl the half-and-half and cornstarch. Stir into liquid in cooker. Cover and cook for 15 minutes more or until thickened. Whisk cheese into liquid in cooker until smooth. Spoon sauce over Brussels sprouts.