Preheat the oven to 425 degrees F (220 degrees C). Tear 3 large sheets of aluminum foil.
Whisk barbecue sauce, ketchup, brown sugar, soy sauce, canola oil, chili powder, black pepper, Cajun seasoning, and Italian seasoning together in a large bowl. Dip a pork chop into the sauce until both sides are coated, then place on the center of a piece of foil. Repeat with remaining pork chops.
Add potatoes and broccoli to the remaining sauce and toss until coated. Scoop equal amounts of the veggie mixture onto each pork chop. Fold the foil into packets and place on a large baking sheet.
Bake in the preheated oven until chops are no longer pink in the center and veggies are tender, 30 to 35 minutes.