Heat the olive oil in a pan over medium high heat. Add the mushrooms and onion, cook until the mushrooms darken and onions start to soften, about 5 minutes. Add the beer, reduce heat and allow to simmer until the beer is almost completely evaporated.
Preheat oven to 400.
Roll out puff pastry on a lightly floured surface, transfer to a baking sheet. Brush the entire pastry with melted butter.
Sprinkle the cheese evenly across the tart, avoiding the outer 1-inch edge.
Spoon the mushrooms and onions over the cheese.
Sprinkle with coarse salt, and thyme.
Bake at 400 until a light golden brown, about 10-12 minutes.