Heat 1 tablespoon of the olive oil in a skillet or on the sauté setting of your multi-cooker. Once the oil is hot, add the vegan sausage and cook until browned, 4 to 5 minutes.
In the same skillet or multi-cooker, add the remaining 2 teaspoons of oil. Add the onion, carrot, celery, and parsley. Cook, stirring often, until the onion is translucent, for about 1 to 2 minutes. Add the garlic and season with the sugar, Italian seasoning, 1 teaspoon each of salt and pepper, and the red pepper flakes (if using). Cook until fragrant, about 1 minute.
Pour in the white cooking wine and continue to cook until most of it evaporates, scraping up any brown bits at the bottom of the skillet or multi-cooker, for about 1 to 2 minutes. Stir in the tomato paste and cook for another 1 to 2 minutes.
If using a slow cooker, transfer the sautéed vegetable mixture to it.
Add the marinara sauce, crushed tomatoes, vegetable broth, non-dairy milk, and pasta shells to the slow cooker or multi-cooker. Stir to combine.
Cover the slow cooker or set the multi-cooker to a low temperature setting. Cook for 4-6 hours on low, or until the noodles are tender. If using a multi-cooker, you can use the slow-cooking function or a specific pasta setting if available.
About 15-30 minutes before serving, add the vegan mozzarella shreds, pesto (if using), and spinach leaves. Stir to combine until the cheese has melted throughout. Taste and adjust seasonings if necessary.
Serve immediately with a few dollops of the tofu ricotta and a sprinkle of basil, if desired.