Prepare the Mint Pesto: In a food processor, combine the fresh mint leaves, basil leaves, pine nuts, grated Parmesan cheese, olive oil, and garlic. Process until smooth. Season with salt and black pepper to taste. Set aside.
Make the Meatballs: In a large bowl, combine the ground lamb, breadcrumbs, grated Parmesan cheese, egg, minced garlic, and 1/4 cup of the mint pesto. Mix until well combined. Form the mixture into small meatballs.
Cook the Meatballs: Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the meatballs and cook, turning occasionally, until browned on all sides and cooked through, about 10-12 minutes. Remove from the skillet and keep warm.
Prepare the Dirty Rice: In the same skillet, add the ground pork or sausage and cook until browned. Add the chopped onion, bell pepper, celery, and minced garlic. Cook until the vegetables are tender, about 5-7 minutes. Stir in the rice, paprika, cayenne pepper, salt, and black pepper. Add the chicken broth and bring to a boil. Reduce the heat, cover, and simmer for 18-20 minutes, or until the rice is cooked and the liquid is absorbed.
Serve and Garnish: Fluff the dirty rice with a fork and transfer to a serving platter. Top with the minty pesto lamb meatballs. Garnish with chopped fresh parsley.