Preheat the oven to 200°C (400°F).
In a large pan, heat the olive oil over medium heat. Add the chopped onion and garlic.
Add the mixed mushrooms and thyme to the pan. Cook for about 8-10 minutes until the mushrooms release their moisture.
Stir in the chopped chestnuts and soy sauce, seasoning with salt and pepper. Cook for another 3-5 minutes.
Remove the pan from heat and let the filling cool slightly.
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.
Fold the pastry over the filling, sealing the edges tightly.
Transfer the Wellington to a baking tray lined with parchment paper. Brush the top with plant-based milk.
Bake for 25-30 minutes until the pastry is golden brown.
Let the Wellington cool for a few minutes before slicing.