Preheat the oven to 425F.

Sprinkle the pork with 1/2 teaspoon of the salt and 1/8 teaspoon of the pepper. Fold the narrow end of the tenderloin under. Combine the parsley, rosemary, and thyme on wax paper. Roll the pork in the herbs, lightly pressing them so they adhere.

Heat the oil in an ovenproof nonstick Dutch oven over medium-high heat. Add the pork and cook until browned on all sides, about 8 minutes. Add the carrots, celery, parsnips, and garlic to the pot. Sprinkle the vegetables with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Pour in the broth.

Roast, tossing the vegetables once or twice, until an instant-read thermometer inserted into the center of the pork registers 160F for medium and the vegetables are tender, about 20 minutes. Let the pork rest for 5 minutes, then transfer to a cutting board and cut into 1/2-inch-thick slices. Serve the pork with the vegetables and any pan juices. Yields 3?4 slices of pork with 1 cup of vegetables per serving.