Preheat oven to 450 degrees. On a large rimmed baking sheet, toss together potatoes, brussels sprouts, and oil; season with salt and pepper. Roast for 15 minutes, tossing once.
Meanwhile, combine apricots, shallot, and jam in a small bowl; season with salt and pepper.
Place pork on a work surface. Holding a chef's knife parallel to work surface, make a pocket by cutting lengthwise down center of tenderloin, stopping about 1/2 inch from other side (avoid cutting all the way through). Open, and stuff with apricot mixture. Spacing evenly, tie 3 to 4 pieces of kitchen twine around pork to close pocket. Season with salt and pepper.
Remove baking sheet from the oven when sprouts and potatoes have roasted 15 minutes. Toss, and push to sides of baking sheet, then place pork in center. Roast until an instant-read thermometer inserted in thickest park of pork (avoiding stuffing) registers 145 degrees, 25 to 30 minutes. Let rest 5 minutes before slicing and serving.