Prepare 2 rectangular cake molds 2.5cm / 1in by 38cm / 15in by 7.5cm / 3 in, spraying with nonstick cooking spray and placing on a full-size sheet pan.
Combine the eggs, sugar, and salt in a 20-qt mixer bowl. Place over a hot water bath and bring the contents of the bowl up to 48°C / 120°F while whisking slowly (don’t whisk too vigorously or else too much air will be incorporated and it will take too long for the ingredients to warm up).
Transfer the bowl to a mixer and whip on high speed for 5 minutes, then turn the speed down to medium and whip for 15 more minutes.
Meanwhile, preheat a convection oven to 350°F (open the vents and turn the fan speed down to low).
Sift the bread flour, pastry flour, and ground spices together twice.
After the eggs have whipped to full volume, take the bowl off the mixer and gently fold in the dry ingredients.
Fold in the butter carefully (so as not to deflate the sponge) and then quickly fold in the diced ginger.
Immediately pour the batter into the prepared molds and spread out evenly with an offset spatula. Bake until golden brown and the sponge springs back when gentle pressure is applied to it at the center of the pan.
Cool to room temperature.
Once it has cooled, trim the crown off the sponge so that it is flush with the top of the mold. Take the molds off.
Freeze the gingerbread for 2 hours and cut into slices 7.5cm / 3in by 1.25cm / .5 in.
Reserve in an airtight container at room temperature. Discard any leftovers after service.