In a separate medium bowl, whisk together flour, salt and baking powder. Add to butter-sugar mixture in three additions, stirring after each to fully incorporate dry ingredients.

Divide dough into two pieces. Press each piece into a 1-inch-thick disk, then wrap tightly in plastic wrap. Chill in the refrigerator for at least 1 hour, or up to 2 days.

Remove and unwrap one disk of chilled dough from the fridge. You have two options here: Either roll out the dough between two large sheets of parchment paper, or roll out on a well-floured surface (sprinkle some flour on top of the dough before rolling out, too). Roll out the dough to 1/4-inch-thick, then use cookie cutters to cut out shapes. Use smaller cookie cutters or a sharp paring knife to cut out smaller shapes in the centers of each cookie. Transfer the cookie cut-outs to the prepared baking sheets, spaced at least 1 inch apart.

Spoon or sprinkle crushed candies into the small cut-outs in each cookie. You'll want to completely fill the holes, but not overfill. Be sure to remove any candy bits that are stuck to the tops of the cookies, or they will dye the cookie.

Bake the cookies for 7 to 9 minutes, or until the edges of the cookies are just set and lightly golden and the candy centers have completely melted. Cool cookies at least 10 to 15 minutes on the cookie sheets so the candy cools enough to remove easily from the sheets. Transfer to a cooling rack to cool completely.

Repeat Steps 5-7 with remaining cookie dough (you can reroll the scraps at least 2x, so use as much dough as you can!).

Pipe icing onto cookies as desired. Allow icing to set completely before stacking, about 30 minutes.

Store finished cookies in an airtight container at room temperature for up to 1 week, or in the refrigerator for up to 10 days.