1. Pat beef tenderloin completely dry with paper towels and season generously with salt and pepper. Let sit at room temperature for 45-60 minutes.

2. Heat butter in a large skillet over medium-high heat. Add shallots and cook until softened, about 3 minutes. Add garlic and thyme, cooking 1 minute more.

3. Add mushrooms to the skillet and cook, stirring occasionally, until all moisture has evaporated and the mixture is paste-like, 15-20 minutes. Deglaze with beef broth and cook until completely dry. Season with salt and pepper, then spread on a baking sheet to cool completely.

4. Heat a cast-iron skillet over high heat until smoking. Add oil and sear the beef for 90 seconds on each side until deeply browned all over. Transfer to a wire rack and cool to room temperature, then refrigerate for at least 30 minutes until completely cold.

5. Lay crêpes on plastic wrap, overlapping to form a rectangle. Spread a thin layer of pâté over the crêpes, then spread the cooled mushroom duxelles evenly over the pâté.

6. Place the cold beef on the prepared crêpe rectangle. Using plastic wrap as a guide, tightly roll the crêpes and mushroom mixture around the beef. Twist the ends to secure and refrigerate for 15-30 minutes.

7. Roll out puff pastry to 1/4-inch thickness on a lightly floured surface, large enough to enclose the beef. Place beef seam-side down in the center of the pastry.

8. Brush pastry edges with egg wash. Fold pastry over the beef, trim excess, and press edges to seal. Fold ends like a present, ensuring no air pockets. Place seam-side down on a parchment-lined baking sheet.

9. Brush entire surface with egg wash (avoiding drips on sides) and score decorative lines on top. Cut small vents for steam. Refrigerate for at least 30 minutes or up to 24 hours.

10. Preheat oven to 425°F (220°C). Apply a second coat of egg wash and sprinkle with flaky sea salt. Bake for 20-25 minutes until deep golden brown.

11. Reduce temperature to 400°F (200°C) and continue baking for 15-20 minutes until internal temperature reaches 120-125°F for medium-rare.

12. Transfer Wellington to a cutting board and rest for 10-15 minutes before slicing. While resting, prepare sauce by reducing beef stock with demi-glace and finishing with butter.

13. Slice the Wellington with a sharp knife and serve immediately with warm sauce and your choice of sides.