Cream the butter in a mixing bowl on medium speed and gradually beat in the sugar. Beat in the egg, vanilla, and salt until well mixed. Stir in the flour, ⅓ at a time, until incorporated. Divide the dough in half, flatten, wrap in plastic, and chill overnight.
Once the dough is chilled, preheat your oven to 375 degrees. Line cookie sheets with parchment paper and coat with cooking spray; set aside.
Remove one chilled dough portion from the refrigerator and place on a lightly floured surface; let stand 10 minutes to soften slightly. Lightly flour the dough, cover with a sheet of waxed paper, and roll to ¼-inch thickness. Remove the paper and use a cookie cutter to cut shapes from the dough; transfer to the prepped cookie sheets. Remove the centers of the cookies using a smaller cookie cutter. Reroll scraps and repeat.
Fill the cut-out part of each cookie with some crushed candy (make sure to get all those nooks and crannies filled too) and bake for 10 minutes, until the edges start to brown and the candy is melted. Cool at least 10 minutes then transfer to cooling racks covered with waxed paper. Repeat with remaining chilled dough.
Store cookies on waxed paper to prevent the candy from sticking.