Add flour, sugar, salt and the cardamom into a food processor. Pulse until well combined.

Add butter, the egg yolk, vanilla and toasted sesame seeds and let the food processor run continuously until it turns into a ball of dough (it might take a minute or so).

Divide the dough in half and form into two logs about an inch and a half thick using either parchment or wax paper or plastic wrap. Refrigerate until very firm (or put it in the freezer for about 20 minutes if you're in a hurry), about an hour.

Turn on the oven to 325 degrees.

Slice the dough into quarter inch rounds and place on ungreased baking sheets.

Bake the shortbread for about 20 minutes or until slightly golden.

Cool the cookies completely on the cookie sheets and serve.