Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the sliced andouille sausage and cook until browned and slightly crispy, about 5-7 minutes. Remove the sausage from the skillet with a slotted spoon and set aside, leaving the drippings in the pan.

Add the chopped onion and bell peppers to the skillet. Cook, stirring occasionally, until softened, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the diced tomatoes (with their juice), chicken broth, Cajun seasoning, smoked paprika, and thyme. Bring the mixture to a simmer and cook for about 5 minutes, allowing the flavors to meld and the sauce to thicken slightly.

Return the cooked sausage to the skillet. Add the peeled and deveined shrimp. Stir everything together and cook for 3-5 minutes, or until the shrimp are pink and cooked through. Be careful not to overcook the shrimp.

Season with salt and freshly ground black pepper to taste. Stir in most of the fresh parsley, reserving some for garnish.

Serve the Cajun shrimp and sausage skillet hot over cooked white rice or with crusty bread for dipping.