In a medium nonstick pan, place two mason jar lids (centers removed). Spray entire pan with cooking spray and place over medium heat. Crack eggs into the centers of lids and lightly whisk with a fork to break up yolk.
Pour water around lids and cover pan. Cook, letting eggs steam, until whites are cooked through, about 3 minutes. Remove lid and top one egg with cheddar. Cook until cheese is slightly melty, about 1 minute more.
Invert egg bun without cheese onto a plate. Top with mashed avocado and cooked bacon. Top with the cheesy egg bun, cheese-side down.