In a large skillet, cook sausage over medium heat until no longer pink. Meanwhile, in another skillet, stir fry the broccoli, onion, celery and red pepper in oil until onion is tender. Stir in the water, barbecue sauce, soup mix, thyme, salt and pepper.
Cut sausage into 1/2-inch slices; add to vegetable mixture. Reduce heat; cook uncovered, for 5-8 minutes, stirring occasionally. Serve over noodles or rice.