Preheat oven to 350 degrees. Line up a baking tray with parchment paper.
Unfold thaw puff pastry and place it on top of prepared tray.
Prepare asparagus and mushrooms by placing them inside a medium bowl, drizzling olive oil and salt to coat. Set aside.
Mix the cheeses with the seasoning. Add more seasoning if you like.
Spread cheese mixture on top of the puff pastry sheet, leaving around 2 inches of the puff pastry border around.
Add asparagus and mushrooms, sprinkle more seasonings and drizzle some olive oil.
Fold each segment of dough over filling, tugging gently so the edge of each segment tightly overlaps the one that came before.
Brush butter around the galette and sprinkle more seasoning to taste.
Bake galette for about 25 to 30 minutes. The time of baking varies depending on your oven. Use an oven thermometer to make sure your oven is reaching the right temperature.
Carefully take it out of the oven, place it on a cooling rack and let it cool for about 10 to 15 minutes before eating.