Prepare a large pot of boiling water. Add the zucchini rounds and boil for 3 minutes. (See Note) Drain the zucchini in a colander and set it aside. Return the empty pot to the stove. Add the butter to the pot and allow it to melt over medium heat. When the butter is hot, sauté the onions until they are tender.Meanwhile transfer the cooked zucchini to the bowl of a food processor. Puree the zucchini until it is smooth. Pour the pureed zucchini back into the pot with the onions. Add the soup base and stir it in with the onions and zucchini. Finally, add the half & half and enough chicken broth to make the soup the consistency that you like.