Step 1: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add ground beef and pork sausage, breaking up the meat with a spoon. Cook until browned, about 8-10 minutes. Drain any excess fat.
Step 2: Add onion, bell pepper, and celery (the 'holy trinity') to the skillet. Cook until softened, about 5-7 minutes. Stir in minced garlic, dried thyme, and cayenne pepper, cooking for 1 minute more until fragrant.
Step 3: Stir in 1 teaspoon of Cajun seasoning and the long-grain white rice. Cook for 2-3 minutes, stirring constantly, to lightly toast the rice.
Step 4: Pour in the chicken broth. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes, or until most of the liquid is absorbed and the rice is nearly cooked.
Step 5: Stir in the shrimp and the remaining 1 teaspoon of Cajun seasoning. Cover and continue to cook for another 5-7 minutes, or until the shrimp are pink and cooked through and the rice is tender.
Step 6: Remove from heat and let stand, covered, for 5 minutes. Fluff the rice with a fork. Stir in fresh chopped parsley. Taste and adjust seasoning with salt and pepper as needed.
Step 7: Garnish with sliced green onions and serve hot.