Heat the olive oil in a large pot over medium heat. Add the diced onion and cook, stirring occasionally, until softened, about 4 to 5 minutes. Add the finely chopped garlic and continue to cook for another minute. Sprinkle in the kosher salt and stir, deglazing the pot with a splash of vegetable broth if anything begins to stick. This builds a flavorful base for your soup.
Stir the tomato paste into the onion and garlic mixture in the pot, cooking for about a minute until it darkens slightly and becomes fragrant. Add the granulated sugar and dried basil, continuing to stir so that everything is well combined.
Pour in both cans of whole tomatoes with their juice and add the remaining vegetable broth. Stir well, bring the mixture to a simmer, cover the pot, and cook for about 20 minutes, stirring occasionally to prevent sticking. If you prefer a bolder flavor, you can add an extra pinch of salt at this stage.
After the soup has simmered, transfer it carefully to a blender along with the cottage cheese. Blend until completely smooth and creamy. Depending on your blender size, you might need to work in batches. Be sure to leave space for steam to escape—blending hot soup can be tricky! I like to remove the blender lid's center cap and loosely cover it with a towel to prevent splatters while allowing steam to release.
Pour the blended soup back into the pot (if needed) and warm through if it has cooled. Serve hot, topped with freshly grated parmesan cheese, torn fresh basil leaves, and a few cracks of black pepper to taste. For an extra touch, I like to add a little drizzle of olive oil or a sprinkle of red pepper flakes for more depth.