Sift the flour, baking powder, cinnamon, and salt into a large bowl. Set aside.
In a stand mixer fitted with a paddle attachment, beat the butter and sugar together until light and fluffy, stopping and scraping the sides of the bowl as needed, about 3 minutes.
Add egg, vanilla extract, and almond extract. Mix on high speed until fully incorporated, about 1 minute.
Add the sifted dry ingredients to the mixer, and mix on low speed until combined, about 2 to 3 minutes. The dough should be soft, but not sticky or unmanageable. If the dough is too sticky to roll, add more flour in ½ tablespoon increments.
Remove the dough from the mixer, and divide it into two equal portions. On a piece of lightly-floured parchment paper, roll out one portion of the dough to ¼-inch thickness. Transfer both the parchment and dough to a large baking tray. Repeat with the remaining dough. Place both trays of rolled dough in the refrigerator, and chill at least three hours, or overnight.
While the dough is chilling, prepare the candies. Separate them by color, and place them into plastic bags. Roughly crush them into small (not powdery or fine) crystals, with a meat mallet or the side of your rolling pin.
After the dough has chilled, preheat the oven to 375˚F degrees and begin cutting the cookies. First, cut out a cookie with the larger cookie cutter. Then, cut out the center of the cookie using a smaller cookie cutter, to create a window. Re-roll the dough and continue cutting cookies until you have used all of the dough. If the dough becomes too soft or sticky, roll it and place it in the refrigerator to chill for 10 to 15 minutes.
Carefully transfer the cookies to a baking sheet lined with parchment, paper, keeping them about 2 to 3 inches apart.
Using a small spoon, fill the centers of the cookies with crushed candy, about 75% full.
Brush the tops of the cookies with whisked egg white, and sprinkle with white crystal sprinkles or coarse sugar (if using).
Bake for 8 to 10 minutes, or until the edges turn a light golden brown.
Remove the cookies from the oven, and let cool on the baking sheet for 10 to 15 minutes, or until the candy centers have set.
Once the cookies have cooled, use a spatula to carefully remove them from the baking sheet, and transfer them to a cooling rack. Cool for another 5 minutes, and serve.