Preheat oven to 200°C/180°C fan-forced. Place buns, cut-side up, on a baking tray. Bake for 10 minutes or until toasted.
Meanwhile, heat a large frying pan over medium heat. Cook bacon, in 2 batches, for 3 minutes each side or until beginning to crisp. Transfer to a large plate and cover to keep warm. Crack half of the eggs into pan and cook for 3 minutes or until the whites are set. Transfer to a large plate. Cover to keep warm. Repeat with remaining eggs.
Place bun bases on a board. Top with egg, bacon, cheese, sauce and avocado. Season with pepper. Sandwich with bun tops. Serve.