Preheat the oven to 350-degrees. Set aside.
Cream sugar and oil with your mixer, then add eggs and your vanilla extract, mixing thoroughly. Set aside.
Whisk together the flour and baking powder in a second bowl. Combine with the sugar/butter mixture in 1/3 increments.
The cookie dough will be kind of crumbly, but turn it out onto parchment paper (parchment paper is important, so don't skip this) and work with it as-is. You don't need to dust the parchment paper with flour, the dough won't stick to it.
Roll the dough to about 1/4-inch thick, but do not work with the cookies any thinner than that as they'll break too easily.
Cut out your cookies.
Do not move the cookies individually, but move the whole parchment paper sheet to the cookie sheet.
Bake the cookies in the oven for 10 minutes. They will not brown, but you don't want them to. If they brown, they will not be soft in the middle. So, just pull them out at 10 minutes.
Leave the cookies on the parchment paper and transfer them to a rack, allowing the cookies to cool completely before you frost them.
In order to make the icing, combine all of the icing ingredients in a small bowl and beat on low speed until smooth.
Place the icing in a decorating bag with your smallest round tip.
Pipe a couple of odd shapes for eyes, different on each cookie. Remember Jack's eyes are not round circles, but oblong, expressive shapes.
Pipe a couple of oblong shapes for the nose holes. Jack's nose holes are really just slits, but try to leave a fair size hole area. You can always fill it in with more white later.
Pipe an edge line all the way around the outer edge of each cookie and immediately fill it in, covering the skull's whole face, with the exception of the eyes and nose slits.
Allow this layer of icing to dry for 2-3 hours.
With the black gel icing, fill-in the nose slits and eye holes, adding eyebrow shapes.