Season pork with salt and pepper. Warm oil in large skillet with lid over medium-high heat; add tenderloins and cook until browned on all sides, 8-10 minutes. Remove pork to a plate and set aside.
Return skillet to medium heat and add apple juice, honey and ginger, scraping up any browned bits on the bottom of the skillet. Stir in carrots. Return pork to skillet, nestling it into carrots. Reduce to simmer, cover and cook 5 minutes.
Add the apples, cover, and continue to cook until the internal temperature of the pork reaches between 145 degrees F (medium rare) and 160 degrees F (medium) and the carrots and apple are tender, about 5 minutes. Remove the pork from the skillet and let rest 5 minutes. Meanwhile, season carrot-apple mixture with salt to taste. Slice pork and serve with carrots, apples, and pan sauce.