Heat a 10-inch non-stick skillet to just under medium heat.
Add a half tablespoon of butter and spread it out over the pan.
Add the sliced mushrooms and diced shallot to the pan and season well with sea salt and pepper. Cook stirring occasionally until the mushrooms have browned (about 5 mins).
Remove the veggies from the skillet and wipe with a paper towel.
Add the remaining butter to the pan and spread it out over the pan.
Season the beaten eggs with sea salt and pepper, then pour them into the middle of the pan.
Let the eggs sit undisturbed for a couple of minutes so they begin to set.
Using a spatula, loosen up the edges of the omelette from the sides of the pan, then while lifting the edge gently and tipping the pan down let some of the uncooked eggs pour in. Do this in a few places around the pan.
The idea is to get more egg under the pan to cook.
Let the omelette cook for a minute or 2 to firm up.
When the top of the omelette is almost set, add the mushrooms, shredded gruyere cheese and chopped chives to one half of the omelette then gently lift the other half to cover.
Let the omelette cook another couple of minutes until the cheese melts then serve garnished with pea shoots.