Place the oven rack to low/medium. Place a baking stone in the oven if you will be using one. Preheat the oven to 400 degrees Fahrenheit.
Remove the dough from the refrigerator, and set on a counter to reach room temperature while you are preparing the filling.
Prepare the mushrooms, slice and stem, and place in a bowl. Set aside.
Heat a 12" skillet to medium, add 2 tablespoons of olive oil. Add the leeks and thyme, cover, stirring occasionally, until leeks are tender and beginning to brown, about 5-7 minutes.
Add the leek/thyme mixture to the bowl with mushrooms. Add the crême fraîche and Dijon mustard, and salt and pepper to season. Mix together. Set aside.
Roll out the dough onto a floured surface, until 1/8 inch thick. Place on the prepared baking sheet, lined with parchment paper. Cut the square edges to create a circle. Brush the dough with 1 teaspoon olive oil.
Place half of the filling into the center of the dough, leaving 1 1/2 -2 inches free as that will be the edge. Then add half of the Gorgonzola. Follow with the remaining filling and the remaining Gorgonzola. Drizzle with 1 teaspoon olive oil.
Fold the edges of the dough onto the filling, overlapping as you make your way around the galette.
Brush with the beaten egg, and sprinkle evening with flaky sea salt.
Reduce the oven to 375 and immediately place the galette in the oven. Set the timer for 30-35 minutes, and rotate once during this time.
Remove from the oven when the crust is brown to your liking as well as the top of the filling. Place on a baking rack to cool for 10 minutes. Sprinkle with minced parsley, and slice into wedges. Enjoy!