Add the butter and sugar to a large bowl (or the bowl of your stand mixer) and beat until the mixture is light and fluffy, about three minutes, using a hand mixer or the paddle attachment on your stand mixer. Scrape down the sides as few times as needed.
Add the egg, molasses, and vinegar. Beat to combine well. The mixture will look a bit curdled.
Add the flour, baking soda, salt, ginger, cinnamon, and cloves to the bowl and mix to combine well. The dough should come together when you press it in your hands and shouldn't be crumbly. If anything it'll still be a little tacky to the touch. That's ok.
Divide the dough into two even pieces, wrap each piece of dough in plastic wrap, and refrigerate for 30 to 90 minutes. Don't skip this step, it helps the cookies to keep their shape.
When the dough is done chilling, preheat oven to 350 degrees. Working in sections, roll the dough to ½ inch thick on a floured surface; cut into desired shapes.
Place shapes on a baking sheet lined with parchment paper or a baking mat. Gather and reroll "scraps" of dough as needed, using all of the dough.
Bake at 350 degrees for 9-11 minutes. Let the cookies cool on the pan for 5 minutes, and then move to a cooling rack.
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