Thaw puff pastry sheet according to directions on the package (2 hours at room temperature).
Preheat oven to 400 degrees.
When the puff pastry is nearly ready to roll out, prep the mushrooms (wash and slice), and add oil and butter to a stovetop pan over medium high heat.
Add sliced mushrooms and sauté, stirring occasionally until they begin to crisp and brown—five to 10 minutes. If the mushrooms begin to burn, reduce the heat slightly. *The pan must be hot for the mushrooms to crisp up and for the water they'll release to evaporate.*
At this point, add in minced garlic, kosher salt, pepper and continue cooking.
Once the majority of the mushrooms are crisp and brown, stir in shredded parmesan and mix well.
Remove from heat and set aside.
Roll out puff pastry onto a baking sheet.
Spoon mushrooms over the pastry evenly, leaving a little less than an inch border.
Using a pastry brush, gently wash the pastry border with the beaten egg.
Bake at 400 for 20 minutes, or until the puff pastry is raised and golden.
Garnish with fresh thyme leaves as you like (a teaspoon or two is perfect).
Using a pizza cutter, slice into squares and serve warm. Enjoy!