The dumplings in this case are often referred to as gnudi, effectively ravioli filling cooked like gnocchi. Once you try these little dumplings in a rich tomato soup, you will never need a grilled cheese again.
For the Soup
In a 6-quart Dutch oven, heat the oil and butter over medium-low heat until the butter melts.
Add the onion, garlic, and sun-dried tomatoes and cook, stirring occasionally, until soft but not browned, about 6 minutes.
Add the flour, stir to coat the onion and garlic, and cook for 5 minutes more.
Add the broth, plum tomatoes and their juices, sugar, and thyme and bring to a boil over medium-high heat while stirring the mixture.
Reduce the heat to low, cover, and simmer for 40 minutes.
For the Dumplings
While the soup is simmering, bring a large pot of salted water to a boil. Set up an ice bath.
In a large bowl, mix the goat cheese, Parmigiano, and eggs. Stir in nutmeg, salt, pepper, and flour.
Form the mixture into balls the size of a quarter.
Dredge the formed dumplings in flour to coat, tapping off the excess.
Slide the dumplings into the boiling water, being careful not to overcrowd the water; work in batches if necessary.
After they float to the top and have cooked for about 4 minutes, remove the dumplings using a slotted spoon and place them in the ice bath to set.
When completely chilled, transfer to a tray and refrigerate.
In a Vitamix or other sturdy blender, blend the soup in batches until smooth.
Rinse the pot and return the soup to the pot. Season with salt and pepper.
Set the pot over medium heat and return the soup to a high simmer.
Add the chilled gnudi and cook over medium-low heat for 10 minutes, but do not boil.
Serve warm, with basil chiffonade sprinkled over each serving.