Preheat oven to 425 degrees.
Heat olive oil in a saute pan over medium-high heat. Once the oil is hot, add the mushrooms to the pan. Lay the mushrooms cut side down. Let the mushrooms start to brown.
After 2 minutes, add the asparagus and the leeks to the pan. Toss all vegetables together.
After another 2 minutes, add the garlic and thyme leaves. Adjust the seasoning with salt and pepper, approximately ¾ teaspoon of salt and ¼ teaspoon of pepper.
Take the pan off the heat. The vegetables are only being par-cooked at this stage because they will continue to cook once the galette is in the oven. Let the vegetables cool while preparing the crust.
Combine the ricotta cheese with 6 tablespoons of parmesan cheese and lemon zest. Adjust the seasoning with salt and pepper. The cheese will add a little saltiness to the ricotta so adjust the addition of salt accordingly.
Have a parchment paper-lined sheet pan ready.
On a floured surface, roll the dough into a 12-inch circle. Place it on the parchment paper-lined sheet pan.
With a spatula or spoon, spread the ricotta cheese mixture on top in an approximately 9-inch circle. Add the cooled vegetables on top of the ricotta cheese. There may be liquid in the pan from sauteing the vegetables. Use a slotted spoon so that the liquid drains from the vegetables before adding to the galette. Sprinkle the remaining parmesan cheese on top of the vegetables.
Make an egg wash by thoroughly combining a tablespoon of water with the egg.
Start to fold the edges of the dough over the vegetables. This is a rustic-looking galette so the border of the dough will not completely cover the vegetables. Once the folding is complete, brush the surface of the dough with the egg wash.
Place the sheet pan in the oven and bake for 30-40 minutes. The time will vary on your individual oven. Start checking at the 30-minute mark. The dough should be golden brown. If it looks a little pale, continue baking for another 5-10 minutes.
Once the galette is out of the oven, squirt some lemon juice over the surface of the exposed vegetables. Let the galette cool for a few minutes before you slice it.