Heat oil in a 2 quart sauce pan over medium high heat.
Add onions and garlic and sauté until tender, then add tomatoes, and mush them up a bit, and stir.
Cook over medium heat about 10-15 minutes, until tomatoes are quite soft and breaking down.
Add water, basil, bouillon cubes, salt and pepper, and sugar.
Bring to boil, reduce heat to low, cover and simmer about 20 minutes.
Near the end of the cooking time, heat half and half or milk so that it is hot.
Add hot milk to soup and stir.
Pureé with an arm blender, or do it in batches in a blender.
Strain soup through a sieve or run it through a food mill to eliminate any peels and seeds that remain.
Mix egg with about 1/4 cup flour (amount will depend on how firm you like your dumplings) and salt and pepper to taste, until well combined.
Bring soup to just below boiling and drop in dumplings by very small spoonfuls. Cook about three minutes, or until dumplings float to the surface. Dumplings should be almost like spaetzle, quite small, and soft when cooked.
Serve hot with chopped fresh basil or toasted croutons as a garnish if desired.