Preheat the oven to 400°F (200°C).

Season the beef tenderloin generously with salt and pepper.

In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Sear the beef on all sides until browned, about 3-4 minutes per side. Remove from heat and let cool slightly.

In a bowl, combine the crushed chestnuts, smoked thyme, and a pinch of salt and pepper.

Brush the seared beef tenderloin with 1 tablespoon of olive oil and then roll it in the chestnut mixture, pressing gently to adhere the crust.

Place the crusted beef on a baking sheet and transfer it to the oven. Roast for about 25-30 minutes for medium-rare, or until the internal temperature reaches 130°F (54°C). Adjust the time if you prefer a different doneness.

While the beef is roasting, prepare the charred garlic compound butter. Cut the top off the head of garlic, drizzle with 1 tablespoon of olive oil, and wrap it in aluminum foil. Roast in the oven alongside the beef for about 30 minutes or until the cloves are soft and caramelized.

In a bowl, combine the softened butter, roasted garlic cloves (squeezed out of their skins), fresh thyme leaves, parsley, and lemon zest. Mix well until fully combined. Set aside.

Once the beef is done cooking, remove it from the oven and let it rest for 10 minutes before slicing.

Serve the sliced beef tenderloin topped with a generous dollop of the charred garlic compound butter.