Preheat the oven to 400°F (200°C).

In a large skillet, heat olive oil over medium heat. Add onions and cook until translucent, about 5 minutes.

Add minced garlic and cook for an additional minute until fragrant.

Stir in the chopped mushrooms and cook for 8-10 minutes until they release their moisture and start to brown.

Add chestnuts, soy sauce, thyme, and black pepper. Stir to combine and cook for another 5 minutes.

Remove from heat and let the filling cool slightly.

Roll out the puff pastry on a floured surface to fit a baking dish, about 1/4 inch thick.

Place the filling in the center of the rolled pastry, then fold the pastry over the filling and seal the edges.

Transfer the Wellington to a baking sheet lined with parchment paper. Brush the top with plant-based milk.

Bake in the preheated oven for 25-30 minutes, until golden and puffed.

Let the Wellington rest for 5 minutes before slicing.