Preheat the oven to 350F.
Add all-purpose flour, corn flour, cheddar cheese, parmesan cheese, and olive oil to a food processor. Blend until combined.
With the food processor running, drizzle 1/3 cup hot water. The dough will stick together when pressed. If it doesn't, add a little bit more water.
Dump the dough onto a silicone baking mat (or floured surface) and gather it into a ball.
Roll out the dough half-way using a rolling pin, and move the dough onto parchment paper.
Roll out the dough until it is less than 1/4" thick. Thinner the crispier.
Place the parchment paper with dough onto a baking sheet.
Cut the cracker into your desired shape, either using a cookie cutter or cutting into squares.
Bake for about 12 minutes until edges are golden. Timing will vary based on the thickness of the crackers, so keep an eye on it.
Store in an airtight container. It's supposed to last a week, but we always finished them in one day!