Clean and clean the mushrooms and possibly wash and halve them. Peel onion and garlic and chop finely. Stir eggs and milk until smooth. Season with salt and pepper. Heat the oil in a coated pan and fry the mushrooms for about 3 minutes, stirring occasionally. Remove and season with salt and pepper. Sauté the onion and garlic in the frying fat for about 3 minutes.
Add the mushrooms and pour over the eggs. Bake slowly at medium heat for about 10 minutes. In the meantime, wash the chives, dab dry and cut into fine rolls. Season crème fraîche with salt and pepper. Turn out the omelette onto a plate, add crème fraîche and sprinkle with chives. Serve with fresh baguette