Heat a large pot over medium heat and add a splash of olive oil. Once hot, add the finely chopped yellow onion, cooking for about 5-7 minutes until it's soft and translucent. Stir in minced garlic, tomato paste, and optional crushed red pepper flakes, cooking for an additional 1-2 minutes until fragrant.

Pour in the crushed tomatoes and chicken or vegetable broth, stirring in granulated sugar and dried basil. Raise the heat to bring the mixture to a gentle boil, then reduce to a simmer. Allow it to bubble away for 10-15 minutes. Stir in heavy cream and season with salt and pepper to taste.

In a medium bowl, combine the ricotta cheese, mozzarella, grated Parmesan, and egg. Then, mix in flour, baking powder, garlic powder, salt, and fresh parsley until well-combined. Let the dumpling mixture rest for about 5 minutes.

Once the soup is at a gentle simmer, scoop spoonfuls of the dumpling batter and carefully drop them into the pot. Cover the pot to create a steam effect, cooking for 6-8 minutes.

Ladle the Cheese Dumpling Tomato Soup into bowls, garnishing with extra grated Parmesan and a light drizzle of olive oil or melted butter if desired.