Heat 1 tablespoon of the oil in a large saucepan over medium heat. Add the onion, celery, bell pepper, and garlic; cover and cook, stirring a few times, until softened, about 5 minutes.
Stir in the tomatoes, thyme, marjoram, Tabasco, salt, and water; cover and simmer until the vegetables are tender, about 30 minutes.
Meanwhile, heat the remaining 1-1/2 teaspoons oil in a medium-sized skillet over medium-high heat. Add the vegetarian or vegan sausage and cook, stirring occasionally, until browned all over, about 5 minutes.
Add the sausage to the tomato mixture, along with the beans and parsley. Cook, uncovered, for 10 minutes, stirring occasionally, to heat through, adding more water if the jambalaya becomes too dry.