Melt the butter in a skillet over a low/medium heat. Thinly slice the shallot and add to the skillet, sweating gently until tender.
Step 3
Whilst the shallots are cooking, add the eggs to a mixing bowl along with the grated cheeses, salt and pepper. Beat together well to combine.
Step 4
Pour the beaten egg mixture over the shallots and increase the heat to medium. Allow the egg to settle and start cooking. Using a spatula, gently bring the cooked edges of the omelette inwards, allowing any uncooked egg to flow underneath.
Step 5
Once the omelette is almost cooked through, with a thin layer of liquid remaining on top, transfer to the oven to finish baking for a further 4-5 minutes, until cooked through and golden brown.