Preheat your oven to 200°C (400°F).
Sauté the onion and garlic in a pan until translucent.
Add the chopped mushrooms and cook until they release their moisture.
Mix in the chestnuts, thyme, soy sauce, and Dijon mustard.
Season with salt and pepper to taste, then let the mixture cool.
Roll out the puff pastry on a floured surface.
Place the cooled mixture in the center of the pastry.
Fold the pastry over the filling and seal the edges.
Brush the top with plant-based milk.
Bake in the preheated oven for 30-35 minutes or until golden brown.