In a one-gallon, heavy-bottomed pot, sauté onions and garlic in butter and oil. Stir frequently over low to medium heat until they turn a deep golden brown--about 30 minutes.
Add chicken broth and bouquet garni and bring to a boil. Stir in bread cubes and simmer 10 minutes, until bread is soft.
Remove bouquet garni and puree soup in blender carefully. Strain back into the saucepan. Heat and whisk in more chicken broth or water if the soup is too thick. Add half-and-half. Season to taste with salt and pepper.