Preheat your oven to 400°F (204°C).

Season the beef fillet all over with salt and pepper.

In a large skillet, heat olive oil over high heat. Add the beef fillet and sear on all sides, about 2 minutes per side. Remove from heat and let cool.

In the same skillet, melt the butter over medium heat. Add the mushrooms, garlic, and shallot. Cook for 10 minutes, stirring occasionally, until the mushrooms are soft and golden brown.

Stir in the parsley and thyme and remove from heat.

On a lightly floured surface, roll out the puff pastry into a large rectangle, about 1/4 inch thick.

Spread the mushroom mixture over the puff pastry, leaving a 1-inch border around the edges.

Place the seared beef fillet in the center of the mushroom mixture and carefully wrap the puff pastry around it, sealing the edges with the beaten egg.

Place the beef Wellington on a baking sheet lined with parchment paper, seam side down.

Brush the top and sides of the pastry with the beaten egg.

Bake for 30 minutes, or until the pastry is golden brown and the beef is cooked to your desired doneness.

Let rest for 10 minutes before slicing and serving.