Makes 64 crackers
In a food processor pulse together flour, cornmeal, sesame seeds, salt, and baking powder. Grate in butter using a box grater and pulse until mixture is rough and crumbly. Add Cheddar and 4 tablespoons water and until water is incorporated, adding enough of remaining tablespoon water if necessary to form a soft dough.
On a lightly floured work surface, knead dough in 3 or 4 turns to develop gluten in flour slightly and make dough easier to work with. Form dough into 2 balls and flatten into disks.
Preheat oven to 400F (200C) and line a baking tray with parchment paper.
On a lightly floured surface, roll out half of dough into a 12-inch square (about 1/16 inch thick) and cut out squares 2-inches across, lifting onto prepared baking tray. Repeat with second piece of dough.
Brush squares lightly with egg wash and prick all over with a fork. Sprinkle with salt and sesame seeds and bake until lightly browned, about 13 minutes. Cool before transferring to a plate.
Crackers can be stored for up to 5 days in an airtight container.