Melt the butter in a saucepan over low heat, stir in the garlic, and cook 1 to 2 minutes until soft but not browned. Pour in the cream and bring to a simmer. Whisk in the avocado until smooth, return to a simmer, and add the shrimp.
Cook over medium-low heat just until the shrimp have turned opaque, 5 to 7 minutes. Sprinkle with black pepper, and serve hot.