Heat a large skillet or Dutch oven over medium heat. Add the sliced Andouille sausage and cook until browned. Remove the sausage and set aside.
In the same skillet, add the olive oil, onion, bell pepper, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the riced cauliflower to the skillet and cook for about 5-7 minutes, or until the cauliflower is tender.
Mix in the drained diced tomatoes, chicken broth, smoked paprika, dried thyme, dried oregano, cayenne pepper, salt, and pepper. Add the bay leaves.
Return the Andouille sausage to the skillet and stir to combine.
Reduce the heat and let the jambalaya simmer for about 10 minutes, allowing the flavors to meld together.
Add the shrimp to the skillet and cook until the shrimp are pink and opaque, approximately 5 minutes.
Remove the bay leaves and discard them.
Garnish the jambalaya with chopped parsley before serving.