In a medium saucepan, melt the butter over medium heat. Add the onion and garlic and cook until the onion is translucent, about 5 minutes. Add the flour and cook another 3 minutes, stirring constantly. Whisk in the broth, taking care to avoid lumps. Reduce heat to low.
In a food processor, puree 4 avocados and add to the broth. Chop 1 cup of shrimp and add to the broth. Simmer over low heat for 15 minutes, add the cream, and season with salt and pepper. Meanwhile, cut the remaining avocado half into small cubes. Serve the soup hot or cold, garnished with the chunks of avocado and the remaining whole shrimp.