In a medium frying pan heat the olive oil and butter and cook the mushrooms with thyme leaves, salt and pepper over low heat for 10 minutes.
Process the cooked mushrooms in a blender or a food processor to a paste. Cool and set aside.
On a floured surface roll out the puff pastry into a rectangular shape until 2cm thick or use a ready rolled pastry sheet.
Spread the mushroom paste all over while leaving a 2cm border. Place the vegetarian haggis in the middle of the pastry sheet; brush the exposed border with a beaten egg. Carefully bring one end over while tucking the sides, and then do the same with the other end. The ends of the puff pastry should overlap, pinch them securely and brush all over with an egg wash.
Transfer the Wellington on a parchment lined baking sheet seam side down.
Bake in the preheated oven for 45 minutes until puffed up and golden.