Preheat the oven to 450 degrees F (230 degrees C).

Combine rosemary, garlic, balsamic vinegar, chicken broth, shallot, olive oil, pepper, and salt in a food processor. Blend until slightly chunky.

Rub all sides of tenderloin with 1/2 to 3/4 of the mixture. Place tenderloin into the bottom of a roasting pan.

Roast, uncovered, in the preheated oven, for 15 minutes.

Meanwhile, combine remainder of the rosemary mixture with parsnips, carrots, potatoes, and celery in a large bowl.

Add vegetable mixture to the roasting pan with tenderloin. Reduce oven temperature to 350 degrees F (175 degrees C).

Transfer back to the oven and continue to cook until an instant-read thermometer inserted into the center of the tenderloin reads 145 degrees F (63 degrees C), about 1 hour.

Remove tenderloin from the roasting pan and let rest for 10 minutes.

Meanwhile, return vegetables to the oven and continue to cook until easily pierced with a fork, about 10 minutes more.