Heat the oven to 350 degrees F. Oil or butter an 8 x 8 inch casserole dish.
Bring a large pot of water to a boil. Gently place the collard leaves in the water and cook for about 3 to 5 minutes until just tender. Remove the leaves, drain and cool.
In a large skillet, heat the olive oil over medium-high heat and sauté the onion, celery, bell pepper and garlic for 5 minutes. Add the turkey and spices and cook another few minutes until the turkey is almost cooked through. Add the broth and rice and cook another few minutes until the broth is absorbed. Season the meat with salt and pepper to taste and remove from heat.
Gently lay out a collard leaf on a dry cutting board, stem end facing away from you. Divide the turkey mixture into eight portions. Place one portion of turkey near the stem end of the leaf. Fold in the side edges of the leaf and roll up the collard around the filling, like a burrito. Place the collard roll in the casserole dish, seam side down. Repeat with the rest of the collards and filling. Drizzle barbecue sauce over the top of the rolls, cover with aluminum foil and place in the oven. Bake for about 30 to 40 minutes until the collard rolls are tender. Serve warm.