In a large bowl, cream the softened butter and granulated sugar with an electric mixer until light and fluffy. Beat in the egg and vanilla extract.
Gradually mix in the all-purpose flour and salt until a smooth dough forms.
Divide the dough into two equal discs, wrap tightly in plastic wrap, and chill in the refrigerator for 1 hour.
Separate the hard candies by color. Place them into separate heavy-duty plastic bags, seal tightly, and crush them with a rolling pin into small pieces.
Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper or silicone baking mats.
Roll out the chilled dough on a lightly floured surface to a 1/4-inch thickness. Use a large cookie cutter to cut out the main shapes. Transfer them to the prepared baking sheets.
Use a smaller cookie cutter (about 1-inch wide) to cut a window out of the center of each cookie. Remove the inner dough pieces.
Carefully spoon the crushed hard candy into the hollow center of each cookie, filling it just to the edges of the dough without overfilling.
Bake for 9-11 minutes, or until the cookie edges are pale golden and the candy has completely melted and leveled out.
Let the cookies cool completely on the baking sheet until the candy is entirely hardened before moving them.