Special equipment: Your favorite 1 1/2-inch cookie cutters
Whisk together the egg white, vinegar and 3 tablespoons water in a small bowl; set aside. Refrigerate the egg yolk in a small bowl, covered, until ready to use.
Pulse the flour, cornstarch, salt, baking powder, mustard, paprika and turmeric in a food processor to combine. Add the butter, Cheddar and Parmesan, and pulse until the butter is completely broken up. Pour in the egg white mixture, and pulse until the dough comes together in a ball. (It's OK if it's a little wet.)
Transfer the dough to a large piece of plastic wrap, and pat it into a 1/2-inch-thick round. Wrap it up, and refrigerate to chill and firm up the dough, about 1 hour.
Position 2 oven racks at the top and bottom third of the oven, and preheat the oven to 350 degrees F. Line 2 baking sheets with parchment.
Roll the dough out on a large piece of parchment (to keep it from sticking to the counter) to about 1/8 inch thick. Cut shapes out with a 1 1/2-inch cookie cutter, and transfer the cutouts to the prepared baking sheets, spacing them about 1/2 inch apart. Gather and reroll the scraps and cut out more crackers; repeat with any remaining scraps. (Dust the dough with flour if you find it too sticky.)
Whisk 2 teaspoons water into the egg yolk. Brush the tops of each cracker with the mixture. Sprinkle each with some sesame seeds, poppy seeds and the tiniest pinch of salt.
Bake 2 baking sheets of crackers at a time, until the crackers are deep golden brown on the bottom, about 20 minutes, rotating the sheets about halfway through. Let cool on the baking sheet for a few minutes, then transfer to a cooling rack to cool completely. Bake the remaining cutouts.
Store the crackers at room temperature in an airtight container for up to 2 days, or freeze them for up to 1 week.
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