Preheat oven to 375°F and lightly grease a 9x13-inch baking dish.
In a large skillet over medium heat, cook sausage until browned and crumbly with no pink remaining, about 6–8 minutes.
Add butter, onion, and celery to the skillet and cook until softened and translucent, about 5 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
In a large bowl, combine bread cubes, cooked sausage mixture, sage, thyme, salt, and pepper. Toss until evenly distributed.
Whisk chicken broth and beaten eggs together, then pour over the bread mixture. Stir gently until the bread is evenly moistened but not soggy.
Transfer mixture to the prepared baking dish and spread evenly. Lightly press down to compact.
Bake uncovered for 35–40 minutes, until the top is golden brown and slightly crisp.
Sprinkle with fresh parsley before serving and let rest 5 minutes to set.
