In a large bowl, sift or vigorously whisk together All-Purpose Flour, Baking Powder, Baking Soda, Salt, Ground Ginger, Ground Cinnamon, and Ground Cloves. Set aside.
In a stand mixer with the paddle attachment on medium speed, or in a bowl with an electric mixer, beat Butter, Dark Brown Sugar, Granulated Sugar, and Egg until smooth.
Add Molasses, Vanilla Extract, and optional Lemon Zest and mix until well blended.
Gradually add the flour mixture and beat on low speed until just combined. Stir in a few strokes by hand to ensure all flour is incorporated.
Divide the mound into 2 equal portions. Shape each portion into a disk and wrap in plastic wrap. Refrigerate at least 2 hours or up to 4 days.
Preheat oven to 375 degrees. Line 2 baking sheets with parchment paper or silicone mats.
On a floured surface working with 1 disk at a time, sprinkle dough and rolling pin with flour and roll out dough to 1/4-inch thick. Using gingerbread cookie cutters, cut out cookies.
Carefully transfer to prepared baking sheets using an offset spatula, spacing about 1 1/2-inch apart. Repeat with remaining disk of dough. Gather all scraps, re-roll, and cut out additional cookies.
Bake until the cookies are lightly browned on the bottom, about 7 to 10 minutes. Cool on baking sheet 5 minutes before transferring to wire racks to cool completely.
In a stand mixer with the paddle attachment on medium speed, or in a bowl with an electric mixer, beat Egg Whites and Cream of Tartar until foamy.
Reduce mixer speed to low and gradually beat in Powdered Sugar until blended, then beat on high speed until thick and glossy, about 2 minutes. Frost Gingerbread Cookies as desired.
