Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish and set aside.
Sauté vegetables: In a large saucepan, melt the butter over medium heat. Add diced onion and celery. Cook for 5–7 minutes, stirring occasionally, until softened and fragrant.
Season: Stir in thyme, sage, salt, and black pepper. Cook for another minute to release the herbs’ aroma.
Add liquid: Pour in the chicken broth and mix well to combine.
Add eggs: Remove the pan from heat and stir in the beaten eggs quickly so they blend smoothly without cooking.
Combine with bread cubes: Place the bread cubes in a large bowl. Pour the mixture over them, tossing gently until all cubes are evenly coated.
Transfer to baking dish: Spread the mixture evenly into the prepared dish.
Bake: Place in the preheated oven and bake for about 50 minutes, stirring once halfway through for even browning.
Garnish and serve: Sprinkle with fresh parsley before serving warm.