Preheat the oven to 400ºF or 200ºC and line a baking sheet with parchment paper.

Add the mushrooms to a food processor and pulse until crumbly. Be careful not to over-process. Set aside.

Also, add the walnuts to the food processor and pulse again until crumbly. Do not over-process. Set aside.

Do the same with the spinach. You can also chop it with a knife if you want. Set aside.

Heat the oil in a large skillet, add the onion and garlic, and cook over medium-high heat until they start to brown. 

Add the mushrooms, walnuts, wine, and soy sauce, stir, and cook for 10 to 15 minutes or until most of the liquid has been released from the mushrooms and has evaporated. Stir occasionally.

Incorporate the thyme, salt, pepper, and spinach, stir, and cook for 2 more minutes, stirring occasionally. The filling needs to be quite dry or it will become soggy inside the puff pastry, so cook it for longer if needed.

Unroll the vegan puff pastry onto the lined baking sheet. Add the filling in the center third of the pastry. 

Fold one side of the pastry over the filling, then the other side. 

Carefully fold the pastry over the filling in a burrito style, rolling it from the long end and gently tucking in the ends as you roll. Brush the top of the crust with melted vegan butter or coconut oil.

Bake for 35 to 40 minutes or until golden brown and puffed.