In a large bowl, sift together flour, salt, and baking powder. Set aside.
In bowl of an electric mixer fitted with paddle attachment, beat butter and sugar on medium speed until fluffy, about 3 minutes. Add egg; beat until smooth, 1 minute.
Add reserved flour mixture, and mix on low speed until thoroughly combined. Stir in vanilla. Wrap dough in plastic, and refrigerate for about 45 minutes.
Position two racks in oven; preheat oven to 325 degrees. Line two baking sheets with parchment paper or a Silpat (nonstick baking mat); set aside.
On a well-floured work surface, roll out chilled dough to 1/8 inch thick. Cut out exterior shapes using a cookie cutter or templates. With a metal spatula, transfer whole cookies to the prepared baking sheets. Using tip of a paring knife, make a cutout in center of each cookie to be filled with candy. Using a straw or the narrow end of a plain round pastry tip, cut a hole in the top of each cookie for hanging.
Chop the candies into 1/4-inch pieces. Sprinkle chopped candy in the center of each cookie, filling the hole. Transfer baking sheet to the refrigerator, and chill until cookie dough is firm, about 15 minutes. Place the baking sheet in the oven, and bake cookies until the candy has melted and completely filled the cut-out area, 6 to 8 minutes. Do not let the cookies brown, or the stained-glass effect will not be as brilliant and the candy centers may become bubbly, not clear.
Let the cookies cool on the baking sheet for about 3 minutes, and then use a metal spatula to transfer them to a wire rack to cool completely.
Cookies will keep at room temperature in an airtight container for up to 5 days.