Heat 2 tablespoons of olive oil in a large pot over medium heat. Sauté 1 chopped onion until it becomes translucent, about 5 minutes. Add 2 minced garlic cloves and stir for another minute.

Stir in 4 cups of chopped ripe tomatoes along with 4 cups of vegetable broth. Season generously with salt and pepper. Bring to a gentle simmer and let it cook uncovered for about 20 minutes.

Using an immersion blender, carefully puree the soup until smooth and creamy. Stir in 1 cup of heavy cream and return the soup to low heat.

In a mixing bowl, combine 1 cup of flour, 1 tablespoon of baking powder, a pinch of salt, and 1 cup of shredded cheese. Gradually add about 1/2 cup of water, stirring until you achieve a soft dough.

Carefully drop spoonfuls of the dumpling mixture into the gently simmering soup. Cover and steam the dumplings for 10-15 minutes until they puff up.

Ladle the soup into bowls and garnish with fresh basil or additional cheese.