Preheat the oven to 180 Celsius (360 Fahrenheit) and line a baking tray with baking paper.
Place the mushrooms onto the tray, drizzle them with olive oil, adjust salt and pepper and bake for 20 minutes.
Meanwhile heat a large pan over medium to high heat, add vegan butter. Once melted stir in the onions and cook until caramelized (about 10 minutes). Then, add in the chopped mushrooms and cook for another 10 minutes on high heat. Finally, deglaze with wine.
Next, add vegan cream and parsley and continue simmering until the mass has a paste-like consistency. Adjust salt and pepper and allow to cool briefly.
Unroll the puff pastry. Spread ⅓ of the mushroom paste in a 6x20 cm ( 2.5x8-inch) strip in the center of the puff pastry. Lay the baked mushrooms on top in a single line, stem-side down. Brush the mushrooms with mustard and cover them with the rest of the mushroom paste.
Lift one side of the puff pastry and cover the filling. Do the same with the other one, making a second layer of puff pastry on top. Tuck the short ends of the puff pastry underneath.
(Optional) Decorate the pastry as you want. I like to cut it diagonally with a sharp knife.
(Optional) Set the Wellington into a baking form to help it keep the form.
Brush the pastry with vegan cream, top with salt flakes and some thyme. Bake in the oven for 35 minutes or until golden. Allow to chill at room temperature for 10 minutes before slicing it and serving.