Heat olive oil in a large pot over medium heat. Add diced onion and cook for 3-4 minutes until softened, stirring occasionally, then add minced garlic and cook for 1 minute more until fragrant.
Pour in crushed tomatoes and vegetable broth, stirring to combine completely. Bring the mixture to a gentle simmer and let it bubble for 8-10 minutes to allow flavors to meld together.
Season the broth with dried basil, dried oregano, salt, and black pepper. Add red pepper flakes if you enjoy heat, tasting as you go because heat preferences vary widely.
Gently add refrigerated tortellini directly to the simmering broth, stirring occasionally to prevent sticking. Follow package directions for cooking time, typically 6-8 minutes, until the pasta floats to the surface.
Reduce heat to low and pour in heavy cream, stirring constantly for 2-3 minutes until fully incorporated and the soup reaches a creamy savory tomato tortellini soup consistency. The mixture should not boil once cream is added.
Stir in fresh spinach and balsamic vinegar, cooking for just 1-2 minutes until spinach wilts completely and vinegar's acidity brightens the overall flavor profile beautifully.
Taste and adjust seasonings as needed, adding more salt or pepper if desired. Ladle into bowls and top with fresh Parmesan cheese before serving.