In a large mixing bowl, combine the flour, sugar, and cinnamon and stir to combine. Add the cold, cubed butter and shortening. Using a pastry cutter, cut the butter and shortening into the flour until the mixture resembles crumbs about the size of peas.
Add the ice water, starting with 5-6 tablespoons, and stir to incorporate. Continue adding the water just until the dough comes together. The dough should stick together when pinched between your fingers. Form the dough into two disks and wrap in plastic wrap. Refrigerate for 30 minutes.
Preheat the oven to 425 degrees. Line baking sheets with parchment paper. Set aside.
On a lightly floured surface, roll out one disk of the dough to 1/8-1/4 inch thick. Using cookie cutters, cut the dough into festive shapes and transfer to the parchment-lined baking sheets. (I used both large and small cookie cutters.) Beat the egg with one tablespoon of water and brush the egg wash on the cookies. Decorate with a variety of sugars.
Bake for 9-10 minutes until lightly golden brown. Remove from the oven and cool the cookies on the baking sheets. The cookies will continue to crisp up as they cool. Store in an airtight container.