Prepare the Crust in a Food Processor: Combine the flour, cornmeal, kosher salt, and black pepper in a food processor, then pulse until evenly mixed.
Add the Cold Butter: Cut the very cold butter into 6 pieces, add it to the food processor, and pulse until the butter is broken into small, pea-sized pieces.
Form the Dough: Add one egg and 1 tablespoon of ice water, then pulse again; continue adding ice water 1 tablespoon at a time and pulsing until the dough comes together into a ball, using up to 4 tablespoons if needed.
Shape and Chill the Dough: Remove the dough from the processor, knead it a few times, shape it into a disk, wrap it in plastic wrap, and refrigerate for 30 minutes.
Prepare the Crust by Hand: If using a mixing bowl instead, combine the flour, cornmeal, salt, and pepper, then stir to combine; add the butter pieces and cut them in with a pastry cutter until they are pea-sized.
Finish the Hand-Mixed Dough: Add one egg and 1 tablespoon of ice water, continuing to work the mixture with the pastry cutter; add more ice water 1 tablespoon at a time until the dough comes together, using up to 4 tablespoons if necessary.
Preheat the Oven: Heat the oven to 375°F (190°C).
Roll Out the Dough: Remove the chilled dough from the refrigerator and roll it on a floured surface into a circle about ¼ inch thick.
Transfer the Dough: Place the rolled dough onto a baking sheet.
Cook the Garlic: Warm the olive oil in a large frying pan over medium heat, add the minced garlic, and sauté for 30 seconds.
Cook the Mushrooms: Add the mushrooms to the pan and sauté for 3 minutes.
Wilt the Spinach: Add the baby spinach one handful at a time, allowing it to wilt as you continue adding the remaining spinach.
Season the Filling: Sprinkle the spinach and mushroom mixture with the kosher salt, give it a final stir, and remove the pan from the heat.
Layer the Mozzarella: Arrange the mozzarella slices around the dough, leaving a 2-inch border around the edge for folding over the filling.
Add the Filling: Spread half of the mushroom-spinach mixture over the mozzarella, then sprinkle half of the shredded Parmesan over it.
Complete the Filling: Add the remaining mushroom-spinach mixture and finish with the remaining Parmesan.
Add the Herbs: Scatter a few pieces of fresh rosemary over the filling, if desired.
Fold the Galette: Fold the exposed edge of the dough inward over the filling to create the rustic crust.
Brush with Egg: Beat the remaining egg and brush it over the folded pastry crust.
Bake the Galette: Bake for 45 minutes, or until the crust is golden brown.
Cool and Garnish: Allow the galette to cool for a few minutes before serving, then garnish with fresh rosemary or thyme if desired.
