In a skillet, saute onions and garlic in olive oil and butter over medium high heat for 1 minute In a slow cooker, add vegetable broth, tomatoes, tomato sauce, vodka, salt and sugar. Then add the sauteed onions and garlic. Cover and cook on high heat for 5 hours.
Puree the soup in batches, then stir in half-and-half.
Cover and cook for an addition 20 minute on low heat setting.