In a large bowl, sift or vigorously whisk together flour, baking powder, baking soda, salt, ginger, cinnamon, and cloves. Set aside.
In a standing mixer with the paddle attachment on medium speed, or in a bowl with an electric mixer, beat butter, brown sugar, granulated sugar, and egg, and beat until smooth.
Add molasses, vanilla, and lemon zest and continue mixing until well blended. Gradually add flour mixture and beat on low speed until just combined. Stir 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 a and roll out dough to 1/4-inch thick. Using gingerbread cookie cutters 3 to 5 inches tall, cut out cookies. Use additional flour to prevent sticking.
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. If the dough becomes sticky, refrigerate for 10 minutes.
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. Frost with royal icing (recipe follows).