• For the pastry dough
• Put the flour and salt in the bowl of a food processor.
• Add the butter and pulse 3 or 4 times to make a mixture that resembles coarse cornmeal.
• Add the cold shortening, pulse 3 or 4 times, then drizzle the cold water over the top of the mixture. Pulse the machine until the dough just comes together on the blade. Don’t overblend; you will finish it by hand. There will be specks of butter and shortening visible in the dough, which is good.
• Turn the dough onto a piece of parchment or plastic wrap, and using the plastic wrap, bring the dough together with your hands to form a disc. Wrap well and refrigerate for several hours or overnight. The dough can be frozen for 3 months.
• Take the dough from the refrigerator and let it sit on the counter for ½ hour before rolling it. Lightly flour the counter and flour the rolling pin. Working from the center of the disc of dough and turning it while you work, gently roll it into a 12” circle making sure to keep the counter under the dough floured while you roll.
• Transfer the dough to a 9” x 13” sheet pan and refrigerate until ready.

For the galette

• Cover the sliced leeks with water in a small bowl and soak for a few minutes. Scoop the leeks out and let them drain in a sieve until most of the water is gone and they are relatively dry. 
• Using a medium saute pan and on low heat, melt 3 tablespoons of butter. Add the sliced leeks, ½ teaspoon of salt, and a few grinds of black pepper. Cover with a piece of parchment paper that is big enough to tuck under them slightly to form a seal. Keep the heat low and allow the leeks to cook and soften slowly. Check them a few times and stir. Cook for 5 or 6 minutes, remove from the heat and allow to cool.
• Clean the mushrooms. Remove stems if using shitakes. Slice all the mushrooms into ¼ inch slices. On high heat, add 2 tablespoons of extra virgin olive oil in a medium-sized non-stick sauté pan. Add half of the mushrooms, a bit of salt and pepper, and ½ teaspoon of chopped fresh thyme. Cook for about 4 minutes, stirring often. They will brown nicely. Repeat with the other half of the mushrooms. Remove from the heat.
• Mix the egg with grated cheese and heavy cream, a pinch of salt, and a few grinds of black pepper.
• Take the pastry from the refrigerator and spread the cooked leeks over the bottom, leaving 1½ inches free around the edge of the pastry. Lay the cooked mushrooms over the top of the leeks and pour the egg and cream mixture over the leek and mushrooms. Pull up the sides of the pastry onto the filling, crimping the dough to form the galette.
• Brush the dough with egg white and sprinkle with some salt.
• Place in the center of the oven and cook for 30 minutes, rotating the pan after 15 minutes.
• Remove from the oven when the pastry is golden brown.