Heat 2 tablespoons olive oil in a large 12-inch skillet over medium-high heat. Add 1.5 pounds ground turkey and cook for 6-8 minutes, breaking it up with a wooden spoon until browned and cooked through. Remove turkey from skillet and set aside. In the same skillet, add remaining 1 tablespoon olive oil. Add diced onions and cook for 3 minutes until softened. Add minced garlic and diced bell peppers, cooking for another 4 minutes until peppers are tender. Stir in paprika, cayenne pepper, chili powder, dried oregano, and dried thyme, cooking for 1 minute until fragrant. Return the cooked turkey to the skillet. Add white rice, stirring to coat with the spice mixture. Pour in tomato sauce and 2 cups water, stirring well to combine. Bring mixture to a boil, then reduce heat to low. Cover skillet with lid and simmer for 20 minutes until rice is tender and liquid is absorbed. Remove from heat and stir in heavy cream and half of the parmesan cheese. Season with salt and black pepper to taste. Let stand covered for 5 minutes before serving. Garnish with remaining parmesan cheese and fresh parsley.