Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim the Brussels sprouts and cut them in half, then peel and slice the carrots into half-moons.
Toss the vegetables on the prepared baking sheet with half of the olive oil, sea salt, and black pepper.
Roast the vegetables in the oven for 20 to 25 minutes, tossing halfway through, until they are tender and caramelized.
In a small ramekin, whisk together the dried rosemary, thyme, and garlic powder.
Pat the beef tenderloin dry with a paper towel, rub with the remaining olive oil, and press the herb mixture firmly onto all sides of the meat.
Heat a cast-iron skillet over medium-high heat and sear the beef for 2 to 3 minutes per side until a deep golden crust forms.
Transfer the skillet to the oven for 8 to 10 minutes, or until the internal temperature reaches 135°F for medium-rare.
Remove the beef from the oven and let it rest on a cutting board for at least 5 minutes before slicing and serving with the roasted vegetables.