Heat oil in a small frying pan over medium-high heat. Add onion and bacon. Cook, stirring occasionally, for 3 to 4 minutes or until onion is soft and bacon crisp. Remove to a bowl. Cover to keep warm.
Beat eggs and 2 tablespoons cold water in a bowl until combined. Season with pepper. Preheat grill on high.
Melt half the butter in a small frying pan over medium-high heat. Add half the egg mixture. Tilt pan so egg covers base. Cook for 1 minute or until almost set. Top with half the bacon mixture and half the cheese.
Place pan under grill. Grill until omelette is lightly browned and cheese melted. Remove to a plate. Cover to keep warm. Repeat with remaining egg mixture, bacon mixture and cheese. Serve omelettes with toasted crusty bread.