Bring a large pot of salted water to a boil. Add the elbow macaroni and cook according to package directions until al dente, about 7 to 8 minutes. Drain the pasta well and set aside without rinsing.

Heat the olive oil in a large skillet over medium heat. Add the shredded chicken, BBQ sauce, garlic powder, onion powder, and smoked paprika. Stir everything together until the chicken is well coated and heated through, about 2 to 3 minutes. Season with salt and black pepper to taste, then remove from heat.

In a separate medium saucepan, heat the milk over medium heat until warm with small bubbles forming around the edges. Reduce heat to medium-low and gradually add the shredded cheddar cheese, stirring constantly. Once the cheddar is mostly melted, add the mozzarella cheese and continue stirring until the sauce is completely smooth and creamy, about 3 to 4 minutes total.

Add the drained macaroni to the cheese sauce in the saucepan. Stir well until every piece of pasta is coated in the creamy cheese sauce.

Fold the BBQ chicken mixture into the cheesy pasta, stirring gently to distribute the chicken evenly throughout. Make sure to scrape in all the BBQ sauce from the skillet.

Transfer to serving bowls. Drizzle with extra BBQ sauce if desired and garnish with chopped fresh parsley before serving.