01 - Preheat the oven to 400°F and lightly grease a medium baking dish (about 2 quarts capacity).
02 - In a large skillet over medium heat, melt the butter. Add leeks, carrots, and celery; cook for 6–8 minutes until softened.
03 - Add mushrooms and garlic. Cook for another 6–8 minutes, stirring occasionally, until mushrooms release their moisture and begin to brown.
04 - Sprinkle the flour over the vegetables and stir for 1–2 minutes to coat evenly.
05 - Gradually add the milk and vegetable broth, stirring constantly to avoid lumps.
06 - Bring to a simmer and cook until thickened, about 4–5 minutes.
07 - Stir in the cream, Dijon mustard, thyme, parsley, and season generously with salt and pepper.
08 - Remove from heat and transfer the filling to the prepared baking dish.
09 - Lay the puff pastry over the filling, trimming edges if necessary. Press the pastry gently onto the edges of the dish to seal.
10 - Brush the pastry with beaten egg for a golden finish (omit for vegan).
11 - Cut a few small slits in the pastry to allow steam to escape.
12 - Bake for 30–35 minutes, or until the pastry is crisp and golden.
13 - Let rest for 10 minutes before serving.