Heat the oil in a dutch oven over medium heat. When the oil is hot add the onion, carrot, bell pepper, 1/2 tsp salt and 1/4 tsp pepper. Stir to combine and cook, stirring occasionally, until vegetables are lightly browned and softened, about 10 minutes.
Stir in the garlic and red pepper flakes and cook until fragrant, about 30 seconds. Stir in the tomatoes and vegetable broth. Bring to a boil then reduce heat to medium-low. Cover the pot and simmer, stirring occasionally, for 10 minutes.
Using an immersion blender or regular blender in batches, puree the soup.
Stir in the quinoa and return to a boil. Reduce heat to low, cover the pot and simmer, stirring occasionally, for 20 more minutes or until quinoa is cooked. Season with salt & pepper to taste.
Ladle soup into serving bowls and top with the freshly grated Parmesan cheese.