Heat a large pot over medium heat and add olive oil, allowing it to shimmer. Sauté the diced onion until it becomes translucent and fragrant, about 5 minutes.
Add minced garlic to the pot and cook for another minute, until fragrant and slightly golden, stirring constantly to prevent burning.
Stir in the chopped roasted vegetables, letting them meld with the aromatics for about 3 minutes, which develops their flavor and softens their texture.
Pour in the crushed tomatoes and vegetable broth, stirring well to combine all the ingredients into a bright red, savory broth. Bring the mixture to a gentle boil.
Once boiling, add the small pasta shells and reduce the heat to maintain a gentle simmer. Cook uncovered until the pasta is al dente, approximately 8-10 minutes, stirring occasionally.
Stir in the shredded mozzarella cheese, allowing it to melt into the soup, creating a gooey, cheesy layer that enhances the richness of the dish.
Season the soup with salt and pepper to taste, then turn off the heat. Sprinkle chopped fresh basil over the top for a burst of fresh flavor.
Ladle the hot, bubbling soup into bowls, ensuring each serving gets a generous amount of pasta, cheese, and herbs. Serve immediately and enjoy the comforting flavors.