In a shallow dish, mix together olive oil, soy sauce, basil, garlic, and salt and pepper. Place mushrooms smooth side down in the mixture. Use a basting brush to cover the underside of the mushrooms with the marinade. Let the mushrooms sit in the marinade for about 15 minutes, flipping and basting them once or twice.
Heat a grill to medium-high heat. Add mushrooms to the grill, reserving the marinade, and cook for about 6-8 minutes on each side, or until mushrooms are tender. As the mushrooms cook, continue to brush them with the reserved marinade
Top with cheese and serve with your favorite hamburger toppings and sides.