Rough-chop the onions, carrots and celery and place them in a food processor. Pulse until chopped fine. You can also mince the veggies by hand, but the food processor just makes it quicker. Mincing the veggies fine will help them melt into the soup as they cook, adding body and flavor to the soup.
Cook the pasta until a couple of minutes short of al dente. Drain, rinse under running water, and set aside.
Heat EVOO in large pot or Dutch oven along with the crushed garlic. Saute until the garlic begins to turn a light golden.
Add the soffrito veggies to the pot--carrots, onions and celery. Add some salt and ground black pepper, stir, cover and cook for 10 minutes over medium low heat or until the soffrito has cooked down but has not browned.
Add the rosemary, oregano and red pepper flakes to the pot and mix in.
Add the beans to the pot followed by the tomatoes. Mix.
Add four cups of hot mushroom stock or vegetable broth and bring to a boil. Cover and cook 10 minutes over medium heat.
Stir in the cooked pasta and mix well.
Continue cooking the soup for another two minutes, check seasoning, and add more salt and pepper if needed. Turn off heat and serve hot or warm. Garnish soup bowls with vegan parmesan and, if you want, a drizzle of EVOO.