2 cups all-purpose flour
1/2 teaspoon baking powder
3/4 teaspoon kosher salt, plus more for sprinkling
6 tablespoons unsalted butter, at room temperature
7 1/2 ounces (about 3 1/2 cups) finely grated sharp cheddar
3-5 tablespoons ice water
1 large egg white, lightly beaten
In the bowl of a food processor, combine flour, baking powder, and salt and pulse to combine. Add the butter and cheese and pulse until very well combined. Add water one tablespoon at a time and continue to mix until the dough is just wet enough to hold together when squeezed.
Divide the dough between two pieces of plastic wrap. Press each half of dough into a flat square, wrap well, and chill for at least 30 minutes.
Pre-heat oven to 350 degrees and grease a couple of baking sheets with butter.
Working with one square at a time, roll the dough out to a scant 1/8-inch thick. Using a fluted (or regular) pastry wheel, cut the dough into 3/4 inch-wide strips. Then cut the dough in the other direction to make 3/4-inch squares. Use the flat end of a wooden skewer to poke a hole in the center of each square. Repeat with the remaining dough.
Line baking sheets with the squares, and brush with egg white then generously sprinkle with salt.
Bake until puffed and set and browned on the bottom, about 14 to 16 minutes. (Make sure to cook them well so that the finished crackers are crisp)
Transfer the parchment with the baked crackers onto a cooling rack. Repeat with the remaining crackers. Store the cooled crackers in an airtight container.