Melt butter in a medium saucepan. Add the chopped onion, carrot, zucchini and garlic; cover and cook over medium heat, stirring occasionally, about 5 minutes.

Sprinkle the flour over the vegetables and stir over low heat for 1 minute, or until the flour is fully incorporated.

Add the chicken broth, tomatoes, tomato paste, dill weed, sugar and pepper and bring to a boil.

Reduce heat to medium-low; cover and cook, stirring occasionally, until the vegetables are tender, 15 minutes. Cool to room temperature (*cooling the soup is especially important if you will be transferring it to a blender.)

Transfer the soup to a blender (or use a hand-held immersion blender) and puree until smooth.

Return the puree to the saucepan, add the half and half and cook until the soup is just heated through.