In a large mixing bowl, sift together flour, Parmesan, and salt. Using a pastry blender or fingers, cut the butter into the dry ingredients until the mixture resembles coarse sand. Add cheddar cheese and ice water and mix until dough pulls together. Divide the dough in half, and form each half into a ball or disk. Cover in plastic wrap and chill 30 minutes.
In a large sauté pan, melt butter over medium heat. Add shallots and cook until translucent, 3 to 4 minutes, stirring often. Add mushrooms and sauté 4 to 5 minutes until mushrooms release their moisture and it cooks off. Add spinach and garlic and cook until spinach is wilted, about 8 minutes, stirring often. Add lemon juice and season with salt, to taste. Remove spinach to colander and squeeze off any excess moisture. Allow to cool to room temperature. Add egg, bread crumbs, feta and pine nuts. Stir to combine.
Preheat oven to 400 F. Line a large baking sheet with parchment paper, or lightly grease.
Remove plastic wrap from chilled dough and roll out to 1/4-inch thick, on a lightly floured surface. Cut dough into 4-inch circles. Place 1/3 cup filling on one half of the dough round. Fold the dough over the filling and crimp the edges together. Transfer to prepared baking sheet. If desired, brush the top of the pies with beaten egg. Bake in preheated oven 18 to 22 minutes. Remove from oven and let stand 5 minutes. Serve warm. Serves 6 to 8.