Preheat oven to 350 degrees Fahrenheit.
Toast the sesame seeds in a frying pan set over medium heat, stirring constantly, for approximately 3 - 5 minutes. They are ready when the sesame seeds have browned. Remove from the heat and set aside in a small bowl.
In a medium sized bowl sift together the flour, dry oregano, salt and cayenne pepper.
Add the grated cheese and the sesame seeds to the flour mixture and mix well to combine.
Add the egg yolk, melted butter and 2 tablespoons of cold water. Mix well with your hands until you can shape the dough into a ball that holds together. You may need to add the additional tablespoon of water.
Divide the dough in half for easier handling. Shape into two balls and then roll it out between two sheets of plastic wrap. Roll the dough out to 1/8 inch thickness.
Using a sharp knife, a pizza cutter or another type of rolling cutter, create your cracker shapes. We like to make rectangles which are approximately 1 inch wide and 2 inches long.
Place your crackers on a parchment paper lined cookie sheet and repeat until you have used up all your dough.
Bake your crackers in the middle rack of your oven for between 15 - 20 minutes. The exact cooking time will depend on how thick your crackers ended up being (and of course, on your oven).
Allow to cool on the baking sheet.