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 cheese and 4 tablespoons water and pulse until water is incorporated, adding remaining tablespoon of 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 200°C and line a baking tray with parchment paper.
On a lightly floured surface, roll out first piece of dough into a 12-inch square (about 1/16 inch thick) and cut into 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.