Using a damp cloth, wipe mushrooms of any dirt and grit. Slice thinly.
In a skillet over medium-high heat, heat olive oil. Add mushrooms and cook, turning them midway, for about 4 to 5 minutes or until lightly browned.
Add garlic and cook for about 30 seconds or until softened.
Increase heat to high. Add wine.
Season with salt and pepper to taste. Continue to cook, stirring as needed, until liquid is absorbed.
Spread butter on one side of each of the french bread slices.
Assemble sandwich by placing one slice of cheese on unbuttered side of bread, spoon 1/4 of mushroom mixture, add another slice of cheese and top with another bread slice unbuttered side down.
In a wide, thick-bottomed pan over medium heat or a preheated panini grill, place sandwiches buttered side down.
Grill for about 2 to 3 minutes on each side or until lightly browned and cheese is melted and gooey.