Whisk the eggs in a small bowl with the fresh herbs, kosher salt, and freshly ground pepper.
Heat the omelet pan over medium-high heat and melt the butter with olive oil. Reduce the heat to medium. Pour in the eggs. Stir with a fork until the eggs start to set. Check to see if the eggs are pulling away from the side of the pan. Shake the pan to loosen the omelet.
Fold in 1/2 and serve.