Beat butter, sugar, and molasses in a stand mixer (or very large bowl with a hand mixer) until smooth. Mix in the egg, then add the vinegar, baking soda, salt, and spices. Mix until combined (mixture may look a bit curdled, that's normal.)
Mix in flour, 1 cup at a time, until dough forms. Divide dough into two sections.
Lay out a sheet of Reynolds Kitchens Parchment Paper with SmartGrid on your work surface. Add half the cookie dough and add a second sheet of parchment paper on the top. Use a rolling pin to roll the dough to 1/4" thick, in between the pieces of parchment. Periodically, gently lift the parchment off the layer to make sure it's not sticking. Repeat with second half of dough.
Chill the rolled out dough in the refrigerator for at least 30 minutes.
Preheat oven to 375°F. Line two cookie sheets with Reynolds Kitchens Parchment Paper with SmartGrid. Cut shapes from chilled dough, placing on the prepared pans. Chill another 10 minutes before baking.
Bake for 8-12 minutes, depending on cookie size. Re-roll any scraps of dough and re-chill and repeat.
Cool cookies completely before frosting.