For the egg dish, clean the mushrooms well and put them in a frying pan with a third of the butter. Stir-fry the mushrooms, season with salt and pepper, lower the temperature and sauté without letting the mushrooms dry out.
Heat remaining butter in a saucepan, add eggs, season with salt and pepper and whisk at very moderate temperature until creamy.
Add crème fraîche, continuing to whisk with a wooden spoon until thickened but not burning to the bottom of the saucepan. Place the beaten eggs on a plate, arrange the chanterelles in the center, sprinkle with a little finely chopped parsley-garlic mixture and mix only at the table.