Preheat oven to 350°F with a rack in the center. Spray a half-sheet pan with cooking spray, line it with a piece of parchment paper, and spray the paper too.
Into a large bowl, sift together the flour, ginger, baking soda, cinnamon, cloves, nutmeg, and salt.
In the bowl of a stand mixer, beat the butter with the paddle attachment on medium-high speed until light and fluffy.
Add brown sugar and beat until combined with the butter, stopping to scrape down the sides of the bowl with a spatula as needed.
Beat in the eggs one at a time.
Lower the mixing speed to medium-low and pour in the molasses. Beat until incorporated.
Carefully beat in hot water.
Lower mixing speed to low and gradually spoon in the flour mixture, along with the lemon zest. Mix just until combined.
Pour batter onto prepared baking sheet and smooth with a spatula.
Bake for 20-25 minutes, until a tester comes out clean.
Let gingerbread cool in the pan set over a cooling rack.
Once cooled, remove cake from pan. (If you have a large cutting board, you can place it directly on top of the sheet pan and flip the whole thing over to release the gingerbread onto the cutting board.)
Peel off parchment paper and cut gingerbread into 1-inch squares.