Season the beef fillet with salt and black pepper. Sear in a hot frying pan with olive oil until browned on all sides, then remove and let cool.

In the same pan, add more oil if needed and sauté the garlic and mushrooms until all moisture has evaporated. Add thyme and white wine, cook until dry. Let cool.

Roll out the puff pastry on a floured surface. Spread the mushroom duxelles over the pastry, place the beef in the center, and wrap the pastry around it, sealing the edges.

Preheat the oven to 200°C (400°F). Place the wrapped Wellington on a baking sheet, brush with beaten egg, and bake for 25-30 minutes until golden brown. Let rest before slicing.