In a mixing bowl, combine the finely chopped onion, chopped lettuce (or parsley), salt, and pepper.
Add the beaten eggs and cream to the vegetable mixture, and stir until well combined.
Heat a non-stick skillet over medium heat and add a knob of butter to coat the bottom.
Pour the egg and vegetable mixture into the hot skillet.
Cook until the omelette is thickened but not fully set.
Once the edges start to set, gently fold the omelette in half using a spatula.
Continue cooking for another minute or until the omelette is cooked through but still moist inside.
Slide the omelette onto a hot serving platter.
Serve the Garden Vegetable Omelette immediately while hot.