Preheat the oven to 200°C (400°F).
Heat olive oil in a large skillet over medium heat.
Sauté the diced onion and minced garlic until soft and translucent.
Add the chopped mushrooms and cook until they release their moisture and become golden brown.
Stir in the chopped chestnuts, thyme, and soy sauce; cook for another 3–4 minutes.
Remove the skillet from heat and let the filling cool.
Roll out the puff pastry on a floured surface and shape it into a rectangle.
Place the cooled filling in the center of the pastry and fold the edges over.
Transfer to a baking sheet lined with parchment paper.
Brush the top of the pastry with plant-based milk.
Bake for 25–30 minutes, or until golden brown.