1. In a large skillet, melt 1 tablespoon of butter and 1 tablespoon of olive oil over medium-high heat. Add the shallot and the mushrooms, and saute, stirring every few minutes, until the mushrooms have begun to release their liquids, about 5 minutes. Season the mushrooms with a sprinkle of salt, and add the vinegar. Cook for another 2 minutes, then add the white wine and the thyme, making sure to scrape up any of the mushroom drippings from the pan. Saute until the mushrooms are dark and caramelized, and the liquids have been fully absorbed, about 5 more minutes. Sprinkle with parsley (if using) and set aside. (The mushrooms can be made up to 2 days in advance).
2. In a small bowl, melt the remaining tablespoon of butter, garlic, and additional thyme sprigs in the microwave.
3. Arrange the bread on a work surface and brush on both sides with the garlic butter. Divide the cheese slices among the 4 slices of bread. Top two of the slices with the mushrooms, and sandwich them together with the remaining bread.
4. Heat a grill pan over a medium-high flame and brush it with olive oil. Grill each sandwich one at a time: cook the sandwich on the first side for 2 minutes, pressing down with a spatula. Rotate the sandwich 90 degrees and cook for an additional minute. Flip the sandwich, and repeat on this side. Remove the sandwich when the cheese is properly melted, and you have nice cross-hatch grill marks on the bread.

If you make this, tag @eatunrestricted and #cheesyliving - We'd love to see it!