Heat 1 tablespoon of olive oil in a large saute pan over medium heat. Add the cremini, shiitake and oyster mushrooms and saute for 5 minutes. Add the shallots and sweat until translucent. Add the wine and thyme. Cook until the wine has reduced and the pan is dry, about 5 minutes. Remove the thyme.
Heat a grill pan over medium heat. Grill the slices of baguette until golden brown. Rub the bread slices with the garlic. Drizzle with olive oil and season with salt. Place the bread on a baking sheet. Place 1 to 2 slices of cheese on each piece of bread.
Broil until the cheese is melted, 2 to 3 minutes. Top each toast with 1 heaping tablespoon of the mushroom mixture. Sprinkle with chives.