Heat a smoker to 250°F. Use a mild wood such as oak or pecan so the smoke complements the chorizo and spices.
In a small bowl, combine the breadcrumbs and milk. Let them stand for a few minutes, until the breadcrumbs are moistened.
In a large bowl, mix the ground beef, chorizo, egg, soaked breadcrumbs, onion, tomato paste, cumin, smoked paprika, chipotle powder, salt, and black pepper. Mix just until combined to keep the meatloaf tender.
Lay the meat mixture on a sheet of parchment and shape it into a rectangle about 1 inch thick. Place the Oaxaca cheese log lengthwise down the center. Fold the meat around the cheese and pinch the seam and ends closed so the cheese is fully enclosed.
Set the loaf seam-side down on a smoker-safe tray or directly on a clean smoker rack. Smoke until the center of the meat reaches 155°F, checking with an instant-read thermometer.
Brush the top and sides with the barbecue sauce. Continue smoking until the center reaches 160°F. Rest the loaf for 10 minutes before slicing so the cheese stays mostly inside each piece.