In a food processor, combine the flour, baking, powder and salt. Add the butter and cheese and pulse into a crumbly dough. Mix in 2 tablespoons of water. The dough should hold together when squeezed. If not, add up to 2 tablespoons of water.
Divide the dough in half and pat into a rectangle. Cover tightly with plastic wrap and chill in the refrigerator for at least 30 minutes.
Roll out one rectangle of dough at a time until it is just less than 1/8-inch thick. Using a fluted pastry wheel, cut into 3/4-inch-wide strips and then cut into perpendicular 3/4-inch-wide strips. Use a skewer to poke a hole into the center of each square. Chill in the freezer for 10-15 minutes.
Preheat the oven to 350 degrees F. Line two sheet pans with parchment paper.
Brush the frozen crackers with egg white and sprinkle with salt. Use an offset spatula to transfer them to the prepared sheet pans and carefully break them apart. Bake for 14-16 minutes until the crackers are puffed up and golden brown. If the crackers are fully frozen, they will need to be baked longer.