Preheat your oven to 425°F (220°C).

Pat the beef tenderloin dry with paper towels. Rub the olive oil all over the tenderloin. Season generously with salt and pepper.

In a small bowl, mix together smoked paprika and fresh thyme. Rub this spice mixture all over the tenderloin, ensuring it is evenly coated.

In a large oven-safe skillet, heat a bit of olive oil over medium-high heat. Once hot, add the tenderloin and sear it on all sides until browned, about 3-4 minutes per side.

Transfer the skillet to the preheated oven and roast for about 20-25 minutes, or until the internal temperature reaches your desired doneness (125°F for medium-rare, 135°F for medium).

While the tenderloin is roasting, heat a small skillet over medium heat. Add the chopped shallots and a pinch of salt. Cook, stirring frequently, until the shallots are golden brown and caramelized, about 8-10 minutes.

In a bowl, mix the softened butter, caramelized shallots, and fresh thyme until well combined. Taste and adjust the salt if necessary. Transfer the compound butter to a piece of parchment paper, roll it into a log, and refrigerate until firm.

Once the tenderloin is done cooking, remove it from the oven and let it rest for 10-15 minutes before slicing. This allows the juices to redistribute.

Slice the tenderloin into medallions and serve topped with slices of the caramelized shallot compound butter.