In a medium bowl, whisk together the flour, baking powder, baking soda, salt, ginger, cinnamon, and cloves.
In a large bowl, beat the butter and brown sugar together until creamy.
Add the egg, molasses, and vanilla extract to the butter mixture and mix well.
Gradually add the dry ingredients to the wet ingredients and mix until well combined.
Divide the dough in half and wrap each half in plastic wrap. Refrigerate for at least 2 hours.
Preheat the oven to 350°F (175°C).
On a lightly floured surface, roll out one half of the dough to 1/4 inch thickness.
Use cookie cutters to cut out desired shapes from the dough.
Transfer the cookies to a baking sheet lined with parchment paper.
Bake for 8-10 minutes, or until the edges are lightly browned.
Remove from the oven and let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Repeat with the remaining dough.
Decorate the cooled cookies with icing, if desired.