Preheat oven to 180°C. Line a large baking tray with baking paper. Mash avocado and spread onto bagel bases. Top with chutney and ham. Place onto prepared tray.
Place bagel tops onto tray and carefully crack an egg into the bagel holes, positioning the yolk over the hole. Place tray in oven and bake for 15 minutes or until egg white is just set. Place rocket on top of ham and cover with bagel tops.