Crack the eggs into a small bowl, add salt and pepper; stir gently with a fork until well-beaten, add basil and parsley and stir.
Heat oil in a 12-inch non-stick pan over medium-high heat. Pour the mixture into the hot pan and reduce heat to medium-low. Watch your omelette and as the eggs set; lift the edges with a spatula to check underneath. When it's setting up; you can see a lot of the egg whites cooked.
When the omelette is just about completely set, sprinkle one layer of the cheese over half of the omelette.
Then slip spatula under the unfilled side, fold the omelette over the filled side and wait till cheese melts.
And then gently slide your omelette onto a plate.