Cook bacon until crisp in a skillet set to medium heat, 3-4 minutes per side. Remove strips to a paper towel-lined plate and then crumble. Set aside.
In a medium bowl, beat eggs until well mixed. Set a skillet over medium heat. Once hot, pour in eggs. Cook, stirring frequently, until eggs are set, 3 to 5 minutes. Remove from heat and sprinkle with salt and pepper, to taste.
Toast bagel halves until lightly golden. Top with greens, chopped tomato, scrambled eggs and shredded cheese. Place on a baking sheet.
Preheat broiler. Place sandwiches under hot broiler for 3-4 minutes, or until cheese is melted. Remove from broiler and sprinkle with crumbled bacon and chopped green onion. Serve warm.