Soak the wood chips in water according to the smoker’s instructions. Preheat the smoker to 250°F and prepare it for indirect cooking.
In a small bowl, stir together the breadcrumbs and milk. Let them sit for a few minutes, until the breadcrumbs absorb the milk.
In a large bowl, combine the ground beef, diced Andouille sausage, egg, breadcrumb mixture, onion, Cajun seasoning, and Worcestershire sauce. Mix gently until just combined.
Shape about half of the meat mixture into a thick rectangle on a sheet of parchment paper. Lay the Provolone slices down the center, leaving space around the edges. Cover with the remaining meat mixture and seal the edges well so the cheese is enclosed.
Transfer the loaf to a wire rack or smoker-safe pan. Stir the ketchup, brown sugar, and apple cider vinegar together in a small bowl. Brush half of the glaze over the loaf.
Add the drained wood chips to the smoker. Smoke the meatloaf until its center reaches 160°F, checking with an instant-read thermometer. Brush with the remaining glaze during the final 20 minutes of cooking.
Remove the meatloaf from the smoker and let it rest for 10 minutes before slicing. This helps the juices settle and keeps the Provolone center in place.