Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Heat the oil in a large skillet over medium heat. When hot, add the onion, carrot, celery, mushrooms, and salt. Cook, stirring occasionally, until softened and the mushrooms have released their liquid, about 10-15 minutes. Add the garlic, rosemary, thyme, and soy sauce, and cook, stirring, for 1 minute, until fragrant.
Transfer the cooked vegetables to a mixing bowl to cool until cool enough to handle. Meanwhile, roll the puff pastry into a 10x13-inch rectangle.
Add the flour, peas, ground beef, and walnuts to the vegetable mixture. Use your hands to combine everything evenly.
Transfer the filling to the pastry, then shape it into a log in the center of the pastry. Wrap the long edges of the pastry over the filling so they overlap in the center. Wet your finger and run it along the seam to help it seal closed.
Fold the short ends up and seal the same way. Flip the wellington over onto the prepared baking sheet. Brush with melted butter. Use a sharp paring knife to score three X’s in the top of the wellington to vent.
Bake for 45-50 minutes, until the top is golden and the pastry is flaky and cooked through. A thermometer in the center should register 165°F. Cool for 10 minutes before slicing.
Notes
Store in an airtight container in the fridge for 4 days or in the freezer for 3 months. Reheat in a 400F oven.