In a large pot of salted boiling water, cook the pasta according to package instructions until al dente. Reserve 1 cup of the pasta water before draining.

While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the sliced onions and a pinch of salt. Stir occasionally, cooking for about 15-20 minutes until they start to brown. If using, sprinkle in the sugar to enhance caramelization.

Once the onions are golden and caramelized, stir in the minced garlic, cooking for an additional 2 minutes until fragrant.

Pour in the balsamic vinegar and let it cook for 1-2 minutes until it reduces slightly.

Lower the heat and add the unsweetened plant-based milk, stirring in nutritional yeast, dried thyme, black pepper, and optional red pepper flakes. Allow the sauce to simmer for 2-3 minutes to thicken. If the sauce is too thick, add the reserved pasta water one tablespoon at a time until you reach the desired consistency.

Add the drained pasta to the skillet, tossing well to coat each strand with the rich sauce. Remove from heat and drizzle in the remaining tablespoon of olive oil. Taste and adjust the seasoning, if necessary.

Garnish with fresh parsley and sprinkle vegan parmesan over the top before serving.