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In a medium-sized bowl, beat together the butter, shortening, sugars, baking powder, spices, and salt until light and fluffy.
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Add the egg and molasses, and beat well.
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Mix about half of the flour into the butter mixture. When well combined, add the cornstarch and the remaining flour.
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Divide the dough in half, flattening each half slightly to make a disk. Smooth the edges by rolling the disk along a lightly floured work surface. Wrap in plastic, and refrigerate for 1 hour (or longer), for easiest rolling.
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Preheat the oven to 350°F.
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Take one piece of dough out of the refrigerator, and flour a clean work surface, and the dough.
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Roll it out as thin or thick as you like. For slightly less crisp cookies, roll it out more thickly. We like to roll these cookies 1/8" to 1/4"inch thick. Use flour under and on top of the dough to keep it from sticking to the table or rolling pin.
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Alternatively, place the dough on parchment, and put a sheet of plastic wrap or another piece of parchment over it as you roll, pulling the plastic or parchment to eliminate wrinkles as necessary when rolling; this will keep dough from sticking without the need for additional flour.
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Transfer the cookies to ungreased or parchment-lined baking sheets.
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Bake them just until they're slightly brown around the edges, or until they feel firm, about 10 to 12 minutes.
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Remove the cookies from the oven, and let them cool on the baking sheet for several minutes, or until they're set. Transfer them to a rack to cool completely. Repeat with the remaining dough.