Heat a large sauté pan over medium heat. Add enough oil to coat the pan. When oil shimmers add the onions and cook until softened and translucent, about 15 minutes.

Remove onions from pan and set aside.

Wipe out the pan and re-heat over medium-high heat. Add butter and equal amount of olive oil to the skillet. When melted add the mushrooms and thyme. Season with a light sprinkle of salt. Cook until mushrooms are softened and have released water, for about 8-10 minutes.

Add the balsamic vinegar and reduce the heat to medium-low. Cook for another 5 minutes to slightly thicken the balsamic.

Remove from heat and combine with the cooked onions. Cool to room temperature before assembling.

Preheat your oven to 400°F and line a baking sheet with parchment paper.

Roll pie crust to about a 12” circle on a lightly floured board.

Spoon the mushroom mixture onto the center of the dough, leaving a 2-inch border all around. Evenly spread the cheese over the filling. Gently fold over the crust, overlapping the edges. Gently press the folds together.

Brush the folded edges of the crust with an egg wash or milk.

Bake for 30 minutes or until the crust has become a lovely golden brown and cheese has melted.

Let cool to room temperature, about 20 minutes before cutting and serving.