In a medium bowl, whisk together the flour, salt, and baking powder. Set aside.
Beat butter and sugar with an electric mixer until pale and fluffy. Add egg and vanilla and mix until combined.
Reduce speed to low and gradually add in flour mixture. Mix until dough starts to clump and hold together.
Scrape dough onto a sheet of plastic wrap and use the plastic wrap to form it into a thick, flat disc (avoid touching dough with your hands). Chill for 1 hour.
Separate candy by color and pulverize them separately in a food processor until they reach a sand-like consistency. Place each color into a small bowl.
Preheat oven to 350F and line baking sheets with parchment or silicone mats.
Take 1/4 of the dough and roll it out to 1/8" thickness between 2 pieces of parchment or on a floured surface.
Cut cookies out and place them on your prepared baking sheet using a small spatula. Make a small hole in the top with the blunt end of a wooden skewer. Chill in the fridge while you do the same with the next 1/4 of dough.
Remove cookies from fridge and cut out shapes for the stained glass with a small cutter or a knife. Use a toothpick to pry out any pieces that don't come out.
Using the tip of a small knife or tapered offset spatula, fill each hole with the crushed candy pieces, filling just to the top of the dough. Nudge into corners as needed and be careful not to get any on top of the cookie dough (brush off any excess). Chill for 15mins if cookies have softened.
Bake for 7-10mins (depending on size and thickness of cookies) just until the candy has melted and the edges start to brown. Rotate cookies at 4mins for even baking. Start watching at the 7min mark to make sure the candy doesn't start to caramelize.