Preheat oven to 350°. In the bowl of a mixer, cream the butter, and sugar until combined. Add the egg, oil, and vanilla and beat again. In a separate bowl, whisk the flour, salt, baking soda, and cream of tartar. Add the dry ingredients to the mixing bowl and stir to form a dough. Scoop the dough into 1-inch balls and place on parchment-lined baking sheets. Put some granulated sugar in a shallow bowl. For each cookie, dip the bottom of a drinking glass into the sugar and then press it onto each dough ball to flatten into a 2-inch round. Bake for 12 to 14 minutes, or until golden brown on the edges. These are meant to be a crisp cookie, so do not be afraid to get them nice and golden brown, rather than underbaking, which you might do with a chewy cookie.