Heat olive oil in a large heavy Dutch oven or soup pot over medium heat. Add diced onions, carrots, and celery (mirepoix); sauté for 6 to 8 minutes until vegetables are tender and fragrant. Add minced garlic, Italian herbs, and red pepper flakes; cook for 1 minute.

Pour in the crushed San Marzano tomatoes, chopped sun-dried tomatoes, and vegetable broth. Season with kosher salt and black pepper. Bring to a boil over medium-high heat, then reduce heat to low and simmer uncovered for 8 to 10 minutes to allow the rich flavors to meld together.

Stir in the fresh three-cheese tortellini. Simmer gently for 3 to 5 minutes until the pasta floats to the top and is tender al dente (be careful not to overcook).

Reduce heat to lowest setting. Pour in the heavy cream, grated Parmesan cheese, and fresh chopped basil. Stir until the cream is fully blended and cheese is melted into a velvety broth.

Ladle hot soup into deep bowls. Top each serving with shredded mozzarella, extra shaved Parmesan, fresh basil leaves, and cracked black pepper. Serve immediately with warm crusty garlic bread.