1. Grill the thinly sliced bread or place them under the broiler until toasted. Turn and toast the other side.
2. Rub the bread with the garlic cloves on both sides and set aside.
3. Combine two tablespoons of butter and two tablespoons of olive oil in a small sauté pan over medium-high heat and cook until the butter melts.
4. Add the onions and sauté until soft—approximately 4–5 minutes.
5. Add the garlic and sauté until soft—about 30 seconds. Watch closely and lower the heat if needed to prevent the garlic from burning.
6. Add more butter and olive oil if the pan seems dry and sauté the mushrooms until soft—approximately 3–4 minutes.
7. Stir in the wine.
8. Add the salt, pepper, thyme and ¼ cup of the cheese. Give the mixture a good toss and continue cooking until the wine is absorbed.
9. Adjust the salt, pepper, and thyme to taste.
10. Place a healthy tablespoon of the mushroom mixture on top of each of the toasts and top with the remaining cheese.
11. Place under the broiler until the cheese melts—less than a minute.