For the aioli (garlic mayonnaise) all ingredients must be at the same temperature. Peel garlic and chop very finely. Beat the egg and mustard in a tall beaker with the whisk of the hand mixer.
Whip the oil gradually, then add a thin stream of oil. Stir in garlic and soured milk. Season the aioli with salt and pepper and chill. Clean and possibly wash the mushrooms. Heat the olive oil in a large pan and fry the mushrooms in it in portions, turning vigorously.
Wash the thyme, dab dry and pluck the leaves from the stems. Season mushrooms with salt, pepper and thyme. Serve mushrooms on a plate. Garnish with marjoram if desired. Serve aioli garnished with thyme in a small bowl.