Separate the eggs and set aside the yolks. In a clean bowl, whisk the egg whites until stiff.
Place the egg yolks in a separate bowl with the tarragon and Cheddar cheese and lightly beat.
Heat the butter in a large heavy-based frying pan. Carefully fold the egg white mixture into the egg yolk mixture and add to the pan. Cook for 2–3 minutes over a high heat and then place under a preheated medium-hot grill for 3–4 minutes or until the top is souffléd and lightly golden.
Serve immediately with a crisp salad and crusty bread.