Dice the onion, bell pepper, and celery, and mince the garlic. Set aside.
Heat the oil in a large heavy-bottomed pot over medium heat until shimmering, about 1 minute.
Add the sliced andouille sausage to the pot and cook until browned and crispy at the edges, about 5-7 minutes. Remove and set aside.
In the same pot, add the diced onion, bell pepper, celery, and minced garlic. Cook, stirring occasionally, until the vegetables are softened and fragrant, about 8 minutes. The mixture should smell sweet and look slightly caramelized around the edges.
Add paprika, cayenne, and thyme to the vegetable mixture. Cook, stirring, for about 1 minute until the spices are fragrant.
Stir in the diced tomatoes, sausage stock, and cooked sausage slices. Bring the mixture to a boil, then reduce the heat to low and simmer gently.
Add the rinsed rice to the simmering broth and stir well to combine. Cover the pot with a lid and cook on low heat for about 20-25 minutes, or until the rice is tender and has absorbed most of the liquid.
Check the rice; it should be tender and slightly sticky, with a vibrant aroma of spices and smoky sausage. If needed, cook a few more minutes uncovered to evaporate excess liquid.
Turn off the heat and let the jambalaya rest, covered, for about 5 minutes. Fluff everything with a fork to combine the flavors evenly.
Spoon the hearty, colorful jambalaya into bowls and serve hot, enjoying the smoky, spicy flavors with every bite.