Grate the Fuji apple into a large bowl.
Add vanilla, egg, olive oil and milk. In a separate bowl, combine the brown sugar, cinnamon and flour.
Gradually add the dry ingredients to the wet ingredients until completely mixed (you want it to form a stiff ball of dough). You may need to adjust the amount of milk to get the right consistency. Roll the dough out on a lightly floured surface until it is approximately 1/4 inch thick.
Cut into cute shapes with the cookie cutter of your choice and bake at 350 degrees for 12 to 15 minutes or until golden brown. For a softer cookie, remove immediately, cool, then refrigerate in an air tight container. For a crisp cookie, turn off the oven and leave the cookies in it for an hour or two before refrigerating in an air tight container.