Preheat oven to 200°C or 390°F.
Line a baking tray with foil and place the beetroot on top of the foil. Drizzle with olive oil and season with salt and rosemary, then wrap the beetroot in the foil. Bake for 45 minutes.
Place the mushrooms, shallots, walnuts and garlic in a food processor, and process until fine.
Transfer the mushroom mixture to a frying pan on a high heat. Add the soya sauce, balsamic vinegar, nutritional yeast and thyme, and fry on a high heat for 15 minutes or until all the water has evaporated.
Roll out the pastry on a baking tray. Then spread half the mushroom mixture along a narrow area 1 inch away from the longest edge and roughly 2 inches away from both shorter edges. Place the beetroots on top next to each other and fill in the gaps between them with more mushroom mixture, pressing down as you go to make sure there are no gaps.
Fold the pastry over the filling as tightly as possible and press down around all the edges to seal the pastry together.
Trim away any excess pastry and press down along the edges with the back of a spoon to create a semi circle pattern. You can use any excess pastry to create decorations to place on top of the wellington.
Brush the pastry with vegan milk and bake in the preheated for 25 minutes.