Preheat oven to 350°
In a large mixing bowl, combine butter and sugars and use an electric mixer to combine ingredients
While continuing to mix, slowly add oil and eggs and mix well
Add dry ingredients (flour, cream of tartar, salt) to the bowl and mix until dough pulls away from the sides and forms a ball
Scoop out uniform balls of dough and roll into smooth balls, placing onto a parchment-lined cookie sheet, leaving a bit of space between each cookie.
Wet a clean dishcloth, lightly squeeze out, and fold into fourths. Prepare a shallow bowl with 1/4 c granulated sugar.
Flatten cookies with a smooth-bottomed glass that is just smaller than the size you desire for your cookies. Press the glass onto the damp dishcloth, then into the granulated sugar, and then press into a cookie until the outer edges of the cookie slightly rise up the edges of the glass. Repeat for every cookie.
Bake for 10-12 minutes or until cookies appear set and edges are just starting to brown.