Allow cookie dough to stand at room temperature 10 minutes. Preheat oven to 375 degrees F. Place cookie dough in a bowl. Knead the 2/3 cup flour and 1/2 tsp. of the apple pie spice into dough.
On a lightly floured surface roll dough out to 1/8-inch thickness. Using a variety of lightly floured leaf-shape cutters, cut dough into shapes, rerolling dough as needed.
Lightly coat a 15x10-inch baking pan with cooking spray. In a medium bowl toss together gingersnaps and melted butter. Press crumb mixture into bottom of prepared pan. Bake 5 minutes. Cool on a wire rack.
In a large bowl combine granulated sugar, the 2 Tbsp. flour, and remaining 1 tsp. apple pie spice. Add pears, pomegranate seeds, and vanilla. Toss gently to coat pears with sugar mixture. Add to crust-lined pan. Top with sugar cookie cutouts (keep smaller cutouts nearer the center). Brush cutouts with lightly beaten egg; sprinkle with turbinado sugar.
Bake 30 minutes. Cover loosely with foil; bake 20 to 25 minutes more or until pear filling is bubbly and cookie leaves are golden brown. Cool on a wire rack.