Add shredded cheese, flour, cornstarch, salt, and cayenne to the bowl of a food processor. Close and blend until combined, about 15 seconds. Add cubed cold butter and process until mixture resembles wet sand and butter is in teeny pieced.
Turn processor on and drizzle in cold water. Process until dough forms, about 10-15 seconds. Turn off. Split dough into two halves and form each half into a square of dough. Wrap eat with plastic wrap and chill until more firm. at least 1 hour.
Preheat oven to 350 degrees. Remove one square from the fridge and place onto clean counter dusted with a little flour. Using a rolling pin, roll square until each edge is 9-inches long. Trim the edges so they are smooth, making an 8-inch square. Brush the dough with egg wash and sprinkle with half of the sesame seeds.
Cut square into 8 strips. Cut each strip into four rectangles. Pierce each rectangle with a fork about 4 times. Place onto baking sheet lined with parchment paper. Bake in preheated oven for about 18 minutes or until the tops just begin to brown. Repeat with other square of dough.
Let the crackers cool completely before serving.