Begin by preheating the oven to 350 degrees Fahrenheit (175 degrees Celsius). Prepare two baking sheets by lining them with parchment paper and set aside.

In the bowl of a stand mixer equipped with a paddle attachment, combine the unsalted butter and powdered sugar. Mix on medium-high speed just until the ingredients are blended, which should take about 30 seconds. The mixture does not need to achieve a light and fluffy texture.

Scrape the sides and bottom of the bowl, then add the egg yolk, vanilla extract, kosher salt, and almond extract. Mix on low speed until fully incorporated, approximately 15 seconds. Gradually add half of the flour, mixing on low until combined. Incorporate the remaining flour, continuing to mix on low until a cohesive dough begins to form, roughly an additional 15 seconds.

Transfer the dough to a clean, lightly floured surface. Knead the dough gently three to four times to create a smooth ball. Flatten it into a disc and roll it out to a thickness of about 1/4 inch. Use an offset spatula to lift the dough off the surface before cutting out shapes.

With a decorative cookie cutter approximately 3 inches in diameter, cut out shapes from the dough and place them onto the prepared baking sheets. Next, take a slightly smaller cookie cutter (between 1 ½ to 2 inches in diameter) to cut out the centers of the larger cookie shapes. If needed, a toothpick can be used to remove the dough centers. Gather the cut-out centers and any remaining dough scraps, re-roll them on a lightly floured surface, and repeat the cutting process. Optionally, place any cut dough centers on a separate parchment-lined baking sheet.

Unwrap the hard candies and place candies of similar colors into separate zip-top bags. Using a rolling pin, gently crush the candies inside the bag, ensuring not to grind them into a fine powder; pebble-sized pieces are preferable. Fill each hollowed cookie shape approximately two-thirds full with the crushed candy.

Bake the cookies in the center of the preheated oven until they are set and the candy has melted, which should take about 9 to 10 minutes. For the cut-out centers, reduce the baking time to about 8 minutes. Once baked, allow the cookies to cool on the baking sheets for 10 minutes before transferring them to wire racks to cool completely, which will take an additional 15 minutes.