Beat the soft butter, oil, and sugars in a large bowl with an electric mixer until creamy, about 2-3 minutes. Beat in the eggs and vanilla.
In a separate bowl, whisk the flour, baking soda, cream of tartar, and salt. Dump into the wet ingredients and stir just until combined.
Cover the cookie dough or wrap in plastic wrap and chill for at least 90 minutes (or overnight).
Preheat your oven to 350°.
Use a cookie scoop to portion the dough into tablespoon sized balls. Place dough balls about 2 inches apart on silicone or parchment-lined baking sheet.
Bake at 350 degrees for about 9 minutes, or until set.
Let cool for 3-5 minutes on the pan, then transfer to a wire rack to cool.