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Cut a 2x3-inch oval out of the center of each slice of bread. Reserve the bread centers for another use. Melt butter in a large nonstick skillet over medium heat. Add bread to the skillet. Cook over medium heat, about 2 minutes, or until the bottom of the bread is golden brown. Carefully flip bread slices. Arrange 2 avocado slices on the perimeter of the hole in each bread slice. Break eggs into a custard cup, 1 at a time, then slip the egg into the center of each circle. Season eggs with salt and ground black pepper. Cook over medium heat for 2 minutes. Sprinkle Gruyere cheese on over toast and eggs. Cover and cook for 1 1/2 to 2 minutes more or until egg is desired doneness and cheese is melted. If desired, sprinkle with freshly cracked black pepper.