½teaspoon flavoring extract such as vanilla or almond (optional)
Line 3 baking sheets with parchment paper.
Using smaller cookie cutters, cut a window from each shape. Use a metal spatula to transfer the cookies to the prepared sheets, spacing them 1 inch (2.5 cm) apart. Press the dough scraps together, roll out, and cut out additional shapes. Use a skewer or drinking straw to cut a small hole in the top of each cookie if you intend to hang it. Chill the cookies in the refrigerator or freezer until firm, about 15 minutes.
Bake the cookies according to the Vanilla Sugar Cookies recipe for 16–19 minutes. Let cool completely, about 30 minutes. While the cookies are cooling on the wire racks, spray the parchment-lined sheets with nonstick cooking spray, then place the cooled cookies on the sheets.
In a saucepan over medium-high heat, bring the sugar, the corn syrup, and ½ cup (4fl oz/125ml) water to a boil and continue to cook until the sugar mixture registers 300°F (150°C) on a candy thermometer. Remove from the heat and divide into separate heatproof measuring cups (if making more than one color). Using a wooden spoon, carefully stir in 1 drop food coloring and the extract, if using. Slowly pour the sugar mixture into the cutout center of each cookie, filling it to the thickness of the cookie. Let cool until the center of each cookie has hardened, about 30 minutes.
If hanging the cookies, thread a ribbon through the hole in each cookie. Store the cookies in an airtight container at room temperature for up to 2 days.