Heat the oil in a large skillet set over medium-high. Add the mushrooms and saute until tender, about 4 to 5 minutes. Add the wine and garlic and cook until the wine has almost entirely evaporated. Remove the skillet from the heat; stir in salt, pepper and parsley.
Preheat the oven to 375 degrees F. Place baguette slices on a parchment paper-lined baking sheet. Cut the cheese into thin slices just large enough to fit the top of the baguette slices. Top the cheese with the mushrooms. Bake for 8 to 10 minutes, or until the cheese just begins to melt. Arrange on a platter and serve.
Recipe Options: Instead of using only brown mushrooms, use a mix of sliced mushrooms such as brown, oyster and white button. If you prefer a stronger flavour, use slices of blue-veined cambozola cheese to make these bites instead of milder-tasting Brie. For even more flavourful bites, use slices of a flavoured baguette such as red pepper or olive.