Preheat oven to 375 °F.
In a skillet, melt butter and olive oil. Sauté onion, garlic, mushrooms, broccoli, and celery until soft.
Add shredded chicken, cream cheese, cream, and broth. Stir until smooth and creamy. Season with salt, pepper, and thyme. Pour mixture into a greased baking dish.
Make the crust: In a bowl, combine almond flour, mozzarella, melted butter, egg, baking powder, and salt. Stir until dough forms.
Spread the dough evenly over the filling (use a spatula or damp fingers).
Bake for 25–30 minutes, until top is golden and slightly crisp.
Let cool 5–10 minutes before serving.