Heat a small 8-inch skillet over medium heat. Add a pat of butter when it’s hot enough to sizzle.
Beat one egg in a small bowl. Pour into hot skillet and quickly swirl to coat the bottom of the pan in a thin layer.
Sprinkle goat cheese over top of egg layer. This will probably take you about 30 seconds, at which point the egg is done.
Use a thin spatula to gently fold the egg in half, then in half again to form a quarter circle. Transfer to warm muffin, season with salt and pepper, and top with 3 avocado slices.
Repeat with remaining eggs as desired.