01 - Preheat oven to 400°F.
02 - Heat olive oil in a large skillet over medium heat. Add leeks and sauté for 3–4 minutes until softened.
03 - Add mushrooms and cook for 5–7 minutes until they release their moisture and begin to brown.
04 - Stir in garlic, carrot, and celery; cook for another 3 minutes.
05 - Remove vegetables from pan and set aside.
06 - In the same skillet, melt butter over medium heat. Stir in flour and cook, stirring, for 2 minutes to make a roux.
07 - Gradually whisk in milk and vegetable broth. Bring to a simmer, whisking until thickened.
08 - Stir in cream, Dijon mustard, thyme, salt, and pepper.
09 - Return sautéed vegetables to the pan. Mix well and simmer for 2–3 minutes. Remove from heat.
10 - Transfer filling to an 8x8 inch baking dish.
11 - Drape puff pastry over the filling, trimming excess and pressing edges to seal. Cut a few slits for steam to escape.
12 - Brush pastry with beaten egg.
13 - Bake for 25–30 minutes, or until pastry is puffed and golden brown.
14 - Rest for 5 minutes before serving.