In a small bowl, combine smoked paprika, garlic powder, onion powder, brown sugar, cayenne, salt, and pepper. Pat the ribs dry with paper towels, peel off the back membrane, and firmly press the dry rub onto all sides of the rack.
Place ribs meat-side down on a roasting pan, wrap tightly in heavy-duty aluminum foil, and bake at 275°F (135°C) for 2.5 to 3 hours until the meat is tender and has pulled back from the tips of the bones.
Bring a large pot of generously salted water to a boil and cook the elbow macaroni 1–2 minutes short of al dente. Reserve ½ cup of the pasta cooking water, then drain.
Melt butter in a medium saucepan over medium heat, whisk in flour for 1–2 minutes to form a roux, then gradually whisk in the whole milk until thickened, about 5–7 minutes. Remove from heat, stir in the dry mustard powder, sharp cheddar, and mozzarella until completely smooth; season with salt and pepper.
Stir the drained macaroni into the cheese sauce, pour into a greased 9x13 inch baking dish, and bake uncovered at 375°F (190°C) for 20–25 minutes until golden and bubbling. Rest for 5 minutes before serving.
Carefully open the foil, raise the oven to 400°F (200°C), and brush the ribs generously with BBQ sauce. Bake uncovered for 10–15 minutes until the sauce is caramelized and sticky, then rest for 5–10 minutes and slice between the bones to serve.