Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish or a similar-sized casserole dish.
In a large skillet over medium-high heat, cook the sausage, breaking it up with a spoon, until it’s nicely browned. Drain off any excess grease. Add the dry bread cubes to the skillet with the sausage and toss gently to combine and coat the bread with some of the sausage drippings. Set this mixture aside.
In the same skillet (or a separate one if needed), melt the butter over medium heat. Add the diced onion and celery and cook until softened, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Add the sautéed vegetables and garlic to the sausage and bread cube mixture. Stir everything together gently.
In a separate bowl, whisk together the low-sodium chicken broth and beaten eggs. Pour this liquid mixture over the bread and sausage mixture. Toss gently until everything is evenly moistened.
Fold in the shredded sharp cheddar cheese, chopped fresh parsley, chopped fresh sage, and dried thyme. Season with salt and black pepper to your taste. Toss everything gently to distribute the cheese and herbs throughout.
Pour the stuffing mixture into the prepared baking dish, spreading it evenly. Cover the dish tightly with foil. Bake for 25 minutes.
Remove the foil and continue to bake for another 15-25 minutes, or until the top is golden brown and wonderfully crisp.