Preheat oven to 350°F and grease a 9x13-inch baking dish.
Place cubed cornbread in a large mixing bowl and set aside.
Melt butter in a large skillet over medium heat, then add onion and celery and cook until softened, about 8-10 minutes.
Pour sautéed vegetables over cornbread cubes and toss to combine.
In a separate bowl, whisk together chicken broth, beaten eggs, sage, thyme, salt, and pepper.
Pour broth mixture over cornbread and vegetables, stirring gently until evenly moistened.
Transfer to prepared baking dish and spread evenly.
Bake uncovered for 40-45 minutes until top is golden brown and edges are crispy.
Let rest 10 minutes before serving.