In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar and salt. Beat till combined, scraping sides of bowl occasionally. Beat in egg, corn syrup, lemon peel and lemon extract till combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon. Divide dough in half. If necessary, cover and chill the dough in the refrigerator about 30 minutes or till easy to handle.
On a lightly floured surface, roll half of the dough at a time till 1/8 inch thick. Using a floured 2-1/2- or 3-inch cookie cutter, cut into desired shapes. Place 1 inch apart on a foil-lined cookie sheet. Cut small shapes out of cookie centers. Reroll trimmings.
Separate hard candies by color. Place each color into a small, heavy resealable plastic bag; seal bag. Finely crush candy. Spoon some of the crushed candy into each center cutout, completely filling to the same thickness as cookies.
Bake in a 375 degree F oven for 7 to 8 minutes or till edges are firm and bottoms are very lightly browned. Transfer cookie sheet to a wire rack and let cookies cool on foil. Using a thin metal spatula, carefully remove cookies from foil or peel foil from backs of cookies. Makes 2 to 3 dozen cookies.
If you wish to hang the cookies with ribbon, use a drinking straw to cut a hole in each cookie before baking.