Warm the olive oil in a large pot over medium heat. After 90 seconds, when the oil is hot, add the onion, carrots, and celery. Sauté, stirring regularly, for 7-8 minutes until the vegetables soften, and onions are fragrant.
Add the garlic, oregano, smoked paprika, thyme, and crushed red pepper flakes if using. Cook, stirring continuously, for 1 minute until the seasonings are well distributed amongst the veggies.
Add the diced tomatoes with their liquid, and vegetable stock. Stir to combine, then increase to medium-high heat and bring to a boil. Once boiling, reduce to medium-low heat and maintain a steady simmer for 10 minutes.
Add the drained canned beans, chopped green beans, zucchini, parsley, and pasta. Stir well and continue cooking over medium-low heat for 10–12 minutes, until the pasta is tender and the vegetables are fully cooked.
Stir in the balsamic vinegar, brown sugar, pepper, and salt, adjusting to taste.
Remove from heat. When portioning the soup into bowls, garnish with vegan parmesan and additional parsley if you like.