Clean the mushrooms with a brush and cut into slices. Finely dice shallot.
Leave the bacon slices in a pan (without fat), remove. Put the mushrooms, shallots and 1 tablespoon of oil in the bacon and fry, season with salt and pepper and remove.
Whisk the eggs with the milk, salt and pepper.
Clean, wash and spin dry the field lettuce. Mix the balsamic vinegar, water, a little salt, pepper, sugar and 2 tablespoons of oil.
Heat 1 / 2 tablespoons butter in a large pan. Add half of the egg mixture. Set over a medium heat for about 1 minute, then spread half of the bacon and mushrooms with shallots on top and let set for another 3 minutes. Half overlap the omelette and slide it out of the pan onto a large plate.
Prepare the 2nd omelette in the same way. Mix the salad with the dressing and serve with the omelette.