Step 1: Preheat your oven to 375°F (190°C). Grease a 9×13 inch baking dish.
Step 2: In a medium bowl, combine the shredded cooked chicken with 1 cup of BBQ sauce. Stir until thoroughly coated. Set aside.
Step 3: Bring a large pot of salted water to a rolling boil. Add the elbow macaroni and cook according to package directions until al dente. Drain well and set aside.
Step 4: In a large saucepan or Dutch oven, melt 1/2 cup butter over medium heat. Whisk in 1/2 cup flour and cook, stirring constantly, for 1-2 minutes to form a roux.
Step 5: Slowly pour in 4 cups whole milk, whisking continuously to prevent lumps. Bring to a gentle simmer, whisking, until the sauce thickens, about 5-7 minutes.
Step 6: Remove the saucepan from the heat. Stir in Dijon mustard, smoked paprika, garlic powder, and salt and pepper to taste.
Step 7: Gradually add the shredded cheddar, Monterey Jack, and Gruyère cheeses, whisking constantly until each addition is completely melted and smooth.
Step 8: Add the drained macaroni to the cheese sauce and stir gently until the pasta is fully coated.
Step 9: Spread half of the cheesy macaroni mixture evenly into the prepared baking dish. Top with half of the BBQ chicken mixture.
Step 10: Add the remaining cheesy macaroni mixture over the chicken. Then, top with the remaining BBQ chicken. Drizzle with extra BBQ sauce if desired.
Step 11: In a small bowl, combine 1 cup panko breadcrumbs with 2 tablespoons melted butter. Sprinkle this mixture evenly over the top.
Step 12: Bake for 20-25 minutes, or until the top is golden brown and bubbly.
Step 13: Remove from oven and let rest for 5-10 minutes before serving.