Preheat to 425 ˚F (220 ˚C). Pierce the pork all over with a fork. Combine the brown sugar, sage, garlic, a pinch of salt and a few grinds of black pepper in a bowl; rub all over the pork.

Toss the potatoes, onion, and carrots with 2 tablespoons melted butter on a baking sheet and season with salt and black pepper. Roast, tossing once, until golden, 20 minutes. Set aside.

Heat the remaining butter in a large nonstick skillet over medium-high heat. Add the pork and cook, turning, until golden, 5 minutes; transfer to the baking sheet with the vegetables. Reserve the skillet.

Roast until the potatoes are tender and a thermometer inserted into the center of the pork registers 145˚F ( 65˚C), 11 to 13 minutes.

Transfer the tenderloin to a platter and cover tightly with aluminum foil.

Meanwhile, add the broth to the skillet; bring to a simmer over medium heat, scraping up any browned bits with a wooden spoon. Stir in the mustard, chives, and a few grinds of black pepper.

Slice the pork; drizzle with the pan sauce. Serve with the roasted vegetables.