In a non-stick pan, heat the oil over medium heat. Add in the ham and cook for 2 minutes.
Add the eggs to the pan. Cook, without stirring, until egg mixture begins to set, for approximately 1 minute.
Lightly toast the bagel.
Using a heat-resistant spatula, gently lift the corner of the eggs; tilt pan to allow uncooked egg to flow underneath. Cook until set. Repeat procedure until remaining egg is cooked.
Add the cheese and fold the omelet in half, place on the bagel, cut in half and serve with raspberries.