Heat vegetable oil in a large stockpot or Dutch oven over medium heat. Add the sliced andouille sausage, diced onion, and diced red and green bell peppers. Cook, stirring occasionally, until the vegetables are tender and the sausage is slightly browned, about 4-5 minutes.

Stir in the basmati rice, minced garlic, sweet paprika, dried oregano, onion powder, dried thyme, and the bay leaf. Cook for about 1-2 minutes until the spices become fragrant. Season with kosher salt and freshly ground black pepper to taste.

Pour in the chicken stock, petite diced tomatoes with their juice, tomato paste, and hot sauce. Stir to combine. Bring the mixture to a boil, then cover the pot, reduce the heat to low, and let it simmer gently for about 15 minutes.

Stir in the peeled and deveined shrimp, seasoning again with salt and pepper as needed. Cover and cook until the shrimp turn pink and are cooked through, and the rice is tender, about 5 additional minutes.

Remove from heat, discard the bay leaf, then stir in the chopped fresh parsley. Serve the jambalaya hot.