Heat the large heavy-bottomed pot over medium-high heat and add the sliced smoked sausage. Cook until browned and fragrant, about 5 minutes.
Add chopped onions, bell peppers, and celery to the pot. Stir well and cook until vegetables are soft and translucent, about 8 minutes, making the mixture fragrant.
Stir in minced garlic and spices—paprika, cayenne, and thyme—and cook for about 1 minute until fragrant and slightly toasted.
Pour in crushed tomatoes and chicken broth, bringing the mixture to a gentle simmer with bubbling sounds and warming aroma.
Add the rice to the simmering mixture, stirring well to combine. Reduce heat to low, cover the pot, and let it cook undisturbed for 20-25 minutes, until the rice is tender and has absorbed most of the liquid.
Check the rice; it should be tender and slightly sticky. Fluff it gently with a fork to separate grains.
Add the peeled and deveined shrimp on top of the rice. Cover again and cook for another 5 minutes until the shrimp turn pink and are cooked through.
Remove from heat, stir gently to distribute the shrimp evenly, and taste for seasoning. Adjust with hot sauce or salt if desired.
Sprinkle sliced scallions over the top for freshness and color. Cover and let rest for 10 minutes to allow flavors to meld.
Serve the jambalaya hot, garnished with additional scallions or herbs if desired, and enjoy the hearty, smoky flavors in every spoonful.
