Cut avocado in half and remove pit. Lay avocado halves on their sides and carefully cut lengthwise into 2 thick slices each. Hollow out middles with a paring knife. In a large, nonstick skillet over medium-low heat, melt 1 tablespoon butter. Place avocado slices into skillet and crack an egg into the center. Season with salt and pepper. Cover skillet and cook until egg is cooked the way you like, about 5 minutes for a just runny egg. Sprinkle cheese on top of each slice, cover with lid again and cook until the cheese is melted, a minute more. Garnish with green onions.