Preheat the oven to 400 degrees. Place the bagel cubes on a baking sheet and bake for 10 minutes until turning golden. Remove from the oven to cook and reduce the oven temperature to 350 degrees.
Spray a 9-inch by 13-inch baking pan with non-stick spray.
Combine the butter and olive oil in a large skillet over medium-high heat. Add the onion, celery and garlic. Sauté until the onions become limp and translucent (7-10 minutes).
Add the breakfast sausage, breaking it up as it cooks. Cook until is browns lights, about 2-3 minutes. Add the thyme and cook for another minutes.
Add the salt and pepper. Transfer the skillet mixture to the prepared baking pan. Stir in the bagel cubes.
Combine the chicken broth and maple syrup; drizzle over the dressing mixture and toss the dressing mixture to evenly coat with the broth.
Bake at 350 degrees for 30 minutes covered with heavy foil. After 30 minutes, remove the foil and allow the dressing to cook an additional 15 minutes uncovered until lightly brown.