Prepare marinated mushrooms for the grill. In a deep container, mix soy sauce, mayonnaise, garlic, salt and paprika, black pepper. Pour in the mushrooms and mix thoroughly so that the marinade completely covers the champignons. Leave for 10 hours.
Grill the mushrooms. Thread a few mushrooms onto long skewers or spits. Grill over hot coals for 15 minutes, turning frequently to ensure even grilling.