In a large skillet set over medium-high heat, melt the butter. Add the celery and leeks and cook, stirring, until fragrant and softened, about 5 minutes. Add the mushrooms, sage, thyme, salt and pepper and cook until the mushrooms are soft, 5 minutes. Add the chicken broth and scrape up any brown bits that have formed on the bottom of the skillet, cooking for an additional minute. Remove from the heat and cool slightly.
Bake until golden brown on top, 30 to 35 minutes. Let cool 5 to 10 minutes before serving.