Combine olive oil and butter in a large skillet; cook over medium heat until butter melts. Add pheasant, and sauté until lightly browned. Transfer to paper towels to drain; set aside skillet with oil mixture. Cut a 1/2- inch slice from the bottom of 1 onion; insert cloves, and set aside. Chop remaining onion. Add chopped onion, garlic, and mushrooms to oil mixture in skillet; sauté until tender.
Return pheasant to skillet. Add wine, parsley, bay leaves, thyme, and reserved onion slice. Cover and simmer 30 minutes or until tender. Discard bay leaves and onion slice.
Serve pheasant halves over rice; spoon vegetable mixture over pheasant. Garnish with cabbage.