Melt the stick of butter over low to medium heat in a large sauté pan. Add the chopped celery and onion. Sauté until the celery and onion are soft and fragrant, about 10 minutes. Remove from heat and set aside.
Transfer the toasted bread to a large mixing bowl. Pour the bowl of liquid ingredients (broth, eggs, herbs, seasonings) and the sautéed onions and celery over the brioche bread cubes. Mix until fully combined.