Wash the potatoes, cut into 1 cm thick circles, boil in salted boiling water for 3 minutes. Throw it onto ice immediately, allow to cool, dry.
Rinse all other vegetables and mushrooms, dry. Shallots and carrots to clear. Cut everything into large slices. Beat butter, chopped parsley and peeled garlic in a blender until smooth.
Put vegetables, including potatoes, and mushrooms in a deep bowl, pour with the mixture, cover with cling film, refrigerate for 5 hours, then put on a wire rack and fry on an open grill on both sides until cooked.
Arrange on plates, season with salt and pepper, pour over the remaining marinade.