Preheat the oven to 475 degrees F. Season the pork all over with salt and pepper. Heat 1 tablespoon olive oil in a large ovenproof skillet over medium-high heat. Add the pork and cook, turning, until browned on all sides, about 8 minutes. Remove to a plate.
Wipe out the skillet; add 1 more tablespoon olive oil and heat over medium-high heat. Add the carrots and cook, stirring, until browned around the edges, about 4 minutes. Stir in the broccoli, remaining 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper. Place the pork on top. Transfer the skillet to the oven and roast until a thermometer inserted into the center of the pork registers 145 degrees F, 12 to 15 minutes. Transfer the pork to a cutting board and let rest at least 5 minutes before slicing.
Meanwhile, return the skillet to the stovetop over medium-high heat. Add the cherry pepper slices, brine and maple syrup to the vegetables. Cook, stirring, until the vegetables are glazed, about 1 minute; season with salt.
Slice the pork and season with salt and pepper. Serve with the glazed vegetables.