Preheat the oven to 375 and prepare two sheet pan sized pieces of parchment paper, or use silicone mats.
In a large bowl, sift together flour, baking powder, sugar and salt. Toss in the shredded cheese until evenly combined, then add in the heavy cream and stir until a dough starts to form.
Turn the dough out onto a floured work surface and knead until it comes together, about 5 minutes.
Divide the dough in half and flour each of the pieces of parchment or silicone mat. Roll out each half of the dough to roughly a 11 x 15 inch rectangle, roughly 1/8 inch thick. Repeat with the other piece of dough.
Make the egg wash. In a small bowl, whisk together the egg, egg yolk, water and salt.
Transfer the piece of parchment paper with the rolled out rough to a baking sheet. Using a ruffle edged slicer, a pizza slicer or a knife, cut the dough into 1 inch squares. If you have space, you can separate the rows of crackers a bit so they they separate, but if you don't have space that's ok (they'll break apart easily after baking). Brush the crackers with the egg wash and use the blunt end of a bamboo skewer to poke a hole in the center of each.
Bake each try of crackers until golden brown, 22-26 minutes, checking frequently at the end to be sure they don't burn. Allow them to cool completely before breaking apart (if needed) and storing in an air tight container for up to 1 month.