1) To make the dough: In a large bowl, cream the shortening, butter, and sugar until light and fluffy. Mix in the softened cream cheese, vanilla, and egg, and beat well.
2) In a medium bowl, sift together the flour, ginger, nutmeg, baking soda, and salt. Gradually add the dry ingredients to the butter mixture, beating until well-combined. Cover the dough and refrigerate it overnight, as it will be soft.
3) The next day, remove the dough from the refrigerator and divide it into quarters. Keeping the remaining pieces refrigerated until they're needed, roll out each piece of dough on a lightly floured work surface to a thickness of 1/8 inch. Use a 3 1/2- to 4-inch round cookie cutter to cut the dough and immediately transfer the rounds to greased or parchment-lined baking sheets, leaving a bit of space between them. Now use a smaller (1-inch or so) cutter in the shape of a heart, star, diamond, or what-have-you to cut out the centers. If the dough isn't cold enough, refrigerate the sheets and cut out the centers when the dough is a bit easier to work with.
4) Refrigerate the scraps and re-roll them with the remaining portion of dough, cutting out cookies till all the dough is gone.
5) Preheat the oven to 375°F and bake the cookies for 6 to 7 minutes, or until they're just firm but still somewhat pale and just lightly browned around the outer edges. Let them cool on the baking sheets.
6) To make the candy centers: Place two or three 1-cup oven-proof glass measuring cups ina 375°F oven to warm. In a medium pan, combine the 2 cups sugar, corn syrup, and water, and stir over medium heat until the sugar is dissolved.
7) Next, and without stirring, cook the syrup until it reaches 280°F (the hard crack stage) on a candy thermometer. Remove the syrup from the heat and take one measuring cup from the oven. Pour one-third or one-half of the syrup into the measuring cup and stir in the food coloring and flavoring extract, if desired. Keep the remaining syrup in the pan, over low heat.
8) When the syrup in the cup stops bubbling, hold the cup with a VERY THICK pot holder and pour the syrup in a thin, gentle stream to fill the cookie centers. Stop pouring just as the syrup comes up to the top level of the cookie. Be careful; this is an extremely HOT process and you may need to take a break halfway through to give your hand a rest.
9) Use the second and/or third cup and the rest of the syrup, colored and flavored differently, to fill the centers of the remaining cookies. (If you have any leftover syrup, pour it into small rounds on a piece of parchment or aluminum foil to make hard candies.)
10) Let the cookies cool completely. Loosen them carefully and peel them off the baking sheets. If these cookies are for consumption, store them in a cool, dry place in a single layer in an airtight container. (For show, we've left them uncovered at least 1 month, and they've been just as sturdy as ever. Be sure not to store them near a heat source!)