Prepare your workspace by preheating your oven to 375°F (190°C) and lining a baking sheet with parchment paper. Take the puff pastry out of the freezer to thaw according to package instructions.
Cook the mushrooms properly by working in batches. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add about one-third of the mushrooms and cook until they release their moisture and begin to brown, about 5-7 minutes. Transfer to a large bowl and repeat with remaining mushrooms, adding more oil as needed.
Sauté the aromatics in the same pan using the remaining oil. Cook the onion until translucent, about 5 minutes, then add garlic and cook for another minute until fragrant. Add to the mushroom bowl.
Create the flavor base by returning the mushroom mixture to the pan. Add soy sauce and balsamic vinegar, stirring to coat everything evenly. Cook for another 2-3 minutes until the liquid is mostly absorbed.
Process half the mixture in a food processor until finely chopped but not puréed. This creates a binding texture while leaving some mushroom pieces intact for a meaty bite.
Combine all filling components in a large bowl—processed mushrooms, chopped mushrooms, walnuts, breadcrumbs, herbs, and wild rice if using. Season with salt and pepper. Let cool completely (warm filling will make the pastry soggy).
Assemble your wellington by rolling out one puff pastry sheet on a floured surface to about 11 x 15 inches. Transfer to the prepared baking sheet. Place the cooled filling mixture in the center, forming a compact loaf shape with about 1.5 inches of pastry exposed on all sides.
Create the top crust by rolling out the second pastry sheet to the same size and draping it over the filling. Press the edges of both pastry sheets together firmly, trimming any excess. Crimp the edges with a fork to seal.
Make it golden by mixing plant milk with maple syrup and brushing this mixture over the entire pastry. Cut 3-4 small slits in the top to allow steam to escape during baking.
Bake until perfectly done, which takes about 40-45 minutes or until the pastry is puffed and golden brown. If it’s browning too quickly, tent loosely with foil.
Rest before serving for at least 10 minutes to allow the filling to set. This makes for cleaner slices and prevents the filling from being too hot.