Preheat oven to 350. Place butter and sugars in a large bowl. Using electric mixture at medium speed, cream butter and sugars together. Beat in egg. Continue to beat until mixture is fluffy. Beat in oil, milk, vanilla and root beer concentrate.
In a large bowl whisk together flour, cream of tartar, baking soda and salt. Add to butter mixture and mix until combined. Fold in white chocolate chips.
Drop ~2 TBLS of dough at a time onto ungreased cookie sheets. Bake 10 minutes. Let cool five minutes on the cookie sheet and them remove them to a wire rack to cool completely.