How to Make It
Using an electric mixer, beat the butter and sugar on medium-high speed until fluffy, 2 to 3 minutes; beat in the egg, vanilla, and salt. Reduce speed to low and add the flour, mixing just until combined (do not overmix).
Divide the dough in half, shape into two disks, wrap in plastic wrap, and refrigerate until firm, at least 3 hours.
Heat oven to 350° F.
On a lightly-floured surface, roll out each piece of dough to an ⅛-inch thickness. Using 2- to 2 ½-inch cookie cutters, cut the dough into shapes and place on parchment-lined baking sheets, spacing them 1 inch apart. Using a ¾- to 1-inch cookie cutter, cut out the centers from each cookie. Reroll and cut the scraps as necessary.
Spoon ½ to 1 teaspoon of the crushed candy (depending on the size of the cutout) into the center of each cookie. Bake until just golden at the edges, 7 to 9 minutes. Let cool on the baking sheets for 5 minutes, then transfer to wire racks to cool completely.
Store the cookies, layered between sheets of wax paper or parchment, in an airtight container at room temperature for up to 1 week.