Heat a large heavy-bottomed pot over medium heat and add the oil. Once shimmering, add diced onion, celery, and bell pepper. Cook, stirring frequently, until vegetables are soft and fragrant, about 8 minutes, with edges starting to caramelize slightly.
Add minced garlic, smoked paprika, cayenne, and thyme to the vegetables. Toast the spices for about 1 minute until they release a fragrant aroma, stirring constantly to prevent burning.
Stir in the vegan sausage slices or crumbles. Cook for about 5 minutes, allowing them to brown slightly and develop a smoky aroma.
Add the canned diced tomatoes with their juice and the rinsed rice. Mix everything well, scraping up any browned bits from the bottom of the pot. Cook for 2-3 minutes until the mixture looks darker and fragrant.
Pour in the vegetable broth and stir to combine. Increase the heat to high and bring the mixture to a boil, watching for bubbling and steam.
Once boiling, reduce the heat to low, cover the pot, and simmer gently for about 20 minutes. Check occasionally to ensure it’s bubbling steadily but not boiling over.
After 20 minutes, uncover the pot and check if the rice is tender and the liquid is mostly absorbed. If needed, cook for an additional 5 minutes uncovered to let any excess moisture evaporate.
Remove the pot from heat and let it rest, covered, for 5 minutes to allow flavors to meld. Fluff the jambalaya with a fork, ensuring rice is fluffy and vegetables are evenly distributed.
Serve the vegan jambalaya hot, straight from the pot. Garnish with chopped fresh herbs if desired, and enjoy the hearty, smoky goodness.