Make the Dough
Sift the flour, ginger, cinnamon, cloves, baking powder and salt together in a medium bowl. Set aside.
Put the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until the mixture is light and fluffy.
Switch the mixer to low speed and gradually add the egg, molasses and vanilla extract. Increase the speed to medium and beat until smooth.
Switch the mixer to low speed and add the dry ingredients in 3 additions, pulsing the mixer to incorporate each addition before adding the next one.
Turn the dough out onto a lightly floured work surface. Knead a few times to incorporate any crumbs.
Divide the dough in half. Roll each half into a log about 1.5 inches in diameter and 12 inches long. As you roll, gently push the ends toward the center to prevent air pockets and to keep the logs at an even thickness.
Wrap the logs in plastic wrap and refrigerate until firm, at least 3 hours or up to 3 days.
Bake the Cookies
Preheat the oven to 400°F. Line the bottoms of two 12-by-18 inch sheet pans with parchment paper.
Remove the logs from the refrigerator and unwrap them. Using a ruler to guide you and a sharp knife, cut each log into rounds .25 inch thick. If the dough crumbles as you cut it, reshape each slice. Place the rounds on the prepared pans, spacing them 2 inches apart.
Bake on the middle shelves of the over, rotating the pans 180 degrees halfway through the baking time, until set but soft enough to hold a slight indentation when pressed with a fingertip, about 7-10 minutes. Let cool completely on the pans on wire racks.
Store in an airtight container at room temperature for up to 1 week.