Take the bone-in pork loin rack out of the refrigerator 45–60 minutes before cooking. Pat it very dry all over, especially the fat cap, with paper towels to help it brown and crisp.

Preheat the oven to 450°F (230°C). Line a large roasting pan or sturdy baking sheet with foil for easier cleanup. Place a roasting rack on top if you have one; otherwise you will use the vegetables as a rack.

Scatter the onion, carrot, and celery chunks in the bottom of the prepared pan. Drizzle with a little olive oil and season lightly with salt and pepper. Spread into an even layer to form a bed for the pork.

In a small bowl, combine the minced garlic, chopped rosemary, thyme, kosher salt, black pepper, smoked paprika (if using), Dijon mustard, brown sugar (if using), and about 2 tablespoons olive oil. Stir until a thick, fragrant paste forms.

Place the pork rack on a cutting board, fat side up. Using a sharp knife, lightly score the fat cap in a crosshatch pattern, cutting through the fat but not into the meat. This helps the fat render and crisp in the oven.

Rub the herb paste all over the pork rack, pressing it into the scored fat cap, sides, and around the bones so the meat is well coated on all surfaces.

Nestle the seasoned pork rack on top of the vegetables in the pan, bones facing down and fat side up. Pour the chicken broth or wine into the bottom of the pan, being careful not to pour it over the meat. Roast at 450°F (230°C) for 15–20 minutes, until the top begins to brown and the crust starts to set.

Without opening the oven if possible, reduce the oven temperature to 325°F (165°C). Continue roasting until the internal temperature in the thickest part of the meat (not touching bone) reaches 135–140°F (57–60°C). As a guide, allow about 18–22 minutes per pound after the initial high-heat phase, but rely on a thermometer for accuracy.

Transfer the pork rack to a cutting board and tent loosely with foil. Let it rest for 15–20 minutes. The internal temperature will rise to around 145°F (63°C) and the juices will redistribute, keeping the meat moist.

While the pork rests, skim excess fat from the pan juices. Place the roasting pan over medium heat if it is stovetop-safe, or scrape the vegetables and juices into a skillet. Add a splash more broth or wine, scrape up the browned bits, and simmer for a few minutes to reduce slightly. Taste and adjust seasoning, swirling in a tablespoon of butter if desired.

Using a sharp carving knife, slice the rack between the bones into individual chops or double chops. Serve hot with the pan juices or sauce spooned over the top, along with the roasted vegetables from the pan if you like.