Heat the olive oil in a large Dutch oven over medium heat until shimmering.
Add the sliced chorizo and sauté for about 10 minutes, stirring occasionally, until browned; use a slotted spoon to transfer the chorizo to a paper-towel-lined plate and set aside.
Add the butter to the same pot, then add both onions, diced celery, and both bell peppers; sauté 8–10 minutes until the onions are translucent.
Stir in the minced garlic, minced jalapeño, cayenne, oregano, thyme, and tomato paste, and cook 1–2 minutes until fragrant and well combined with the vegetables.
Pour in the chicken stock and diced tomatoes and bring the mixture to a boil.
Stir in the rinsed rice, return the reserved chorizo to the pot, add the bay leaves, kosher salt, black pepper, and hot sauce; bring back to a boil.
Reduce heat to low, partially cover, and simmer for 25 minutes, or until the rice is nearly tender and has absorbed most of the liquid.
Add half of the chopped basil, half of the scallions, half of the parsley, the lime juice, and the shrimp; stir to combine.
Cover the pot, remove it from the heat, and let the jambalaya steam for 20 minutes so the shrimp finish cooking and flavors meld.
Uncover and garnish with the remaining basil, scallions, and parsley; adjust seasoning with additional hot sauce, salt, or pepper if desired, then serve.