Preheat oven to 400° F (205° C).
Mix all rub ingredients together in a small bowl and then rub onto pork tenderloin.
Heat half of the oil in an oven proof skillet* or dutch oven to medium-high heat. Add pork tenderloin and sear for 2-3 minutes per side. Remove and let rest on a plate. Scrape as much of the burned sugar off the pan as you easily can and discard.
Add remaining oil, potatoes, carrots, sweet potato, and onion. Let vegetables caramelize, stirring every 1-2 minutes for 7-10 minutes. Season vegetables with salt and pepper and then stir in apple slices.
Push vegetables to outer rim and lay pork tenderloin in middle.
Place pan in oven and bake for 25-35 minutes until pork and vegetables are cooked through. The internal temperature of the pork should be 145 – 150° F (63-66° C) since it will continue cooking as it rests.
Remove pan from oven and place pork and vegetables on a serving platter. Cover or tent with foil to keep warm while you make the sauce.
Place the pan on the stovetop and turn the burner to low heat. Add the brandy and use a wooden spoon to scrape up as much of the browned bits as you can.
Add apple juice, bring to a simmer, and reduce to about half a cup (5-7 minutes). Add butter and season with salt and pepper.
Slice pork tenderloin and serve with vegetables and sauce.