Gather and prepare all ingredients as specified. Slice sausage, dice chicken, chop vegetables, mince garlic. Rinse the rice under cold water until the water runs clear; drain well.

Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the sliced Andouille sausage and cook until well browned and slightly crispy, about 5-7 minutes. Remove sausage with a slotted spoon and set aside, leaving rendered fat in the pot.

Add the diced chicken thighs to the pot with the remaining fat. Sear until browned on all sides, about 5-8 minutes. It doesn't need to be cooked through. Remove chicken and set aside with the sausage.

Reduce heat to medium. Add the chopped onion, celery, and green bell pepper to the pot. Cook, stirring occasionally, until softened, about 8-10 minutes.

Stir in the minced garlic, Cajun seasoning, smoked paprika, dried thyme, and cayenne pepper. Cook for 1 minute more until fragrant, stirring constantly to prevent burning.

Stir in the tomato paste and cook for 1 minute, scraping up any browned bits from the bottom of the pot. Pour in the chicken broth and crushed tomatoes. Add the bay leaves.

Bring the soup to a simmer, then return the browned sausage and chicken to the pot. Stir well. Cover partially and let it simmer for 15 minutes to allow flavors to meld.

Stir in the rinsed long-grain white rice. Continue to simmer, uncovered, for another 15-20 minutes, or until the rice is tender and has absorbed some of the liquid, thickening the soup slightly. Stir occasionally to prevent rice from sticking.

Remove the bay leaves. Taste and adjust seasoning if necessary (you might need more salt, pepper, or Cajun seasoning). Ladle hot Jambalaya Soup into bowls. Garnish with fresh chopped parsley and sliced green onions. Serve with a dash of hot sauce if desired.