Mix cooking wine, soy sauce, vinegar, oil, and garlic together in the bottom of a baking dish. Place mushroom caps into the baking dish with the gills facing up. Spoon marinade into the cavities, cover with foil, and marinate for 15 minutes.

Preheat the oven to 400 degrees F (200 degrees C).

Bake in the preheated oven for 25 minutes. Flip mushrooms and bake until mushrooms are tender and juicy, about 8 more minutes.