Preheat the oven to 400°F.

Put 1 tablespoon of the oil, 1/2 tablespoon of the rosemary, thyme, garlic, 1 1/2 teaspoons of the salt and 1/2 teaspoon of the pepper into a small bowl and mix well.

Rub mixture all over beef; set aside.

Heat remaining 1 tablespoon oil in a large skillet over medium-high heat.

Add beef and cook, turning occasionally, until deep golden brown all over, about 10 minutes.

Transfer to a large plate; set aside.

Put potatoes, carrots, remaining 1 tablespoon rosemary, remaining 1 teaspoon salt and 1/4 teaspoon pepper into a large bowl.

Drizzle any remaining drippings from the skillet over potatoes and carrots and toss to combine.

Transfer to a large roasting pan and spread out in an even layer; arrange beef on top.

Heat the same skillet over medium heat.

Add broth and cook, stirring to scrape up any browned bits, for 30 seconds.

Pour pan drippings over beef.

Roast until a meat thermometer inserted in the thickest part of the tenderloin registers 130°F, 20 to 25 minutes.

Transfer beef to a platter, tent with foil and set aside.

Toss potatoes and carrots and continue to roast until tender and golden brown, about 10 minutes more.

Transfer to a serving bowl.

Cut beef into slices and serve with any juices drizzled over the top.