Preheat the oven to 350 degrees F. and line cookie sheet with parchment paper or silpat mat.
In stand mixer with flat paddle attachment, beat together sugar and butter for 3-5 minutes. To this, add milk and whipping cream,1/4 cup at a time. Once mixture is smooth, add in the vanilla.
In a separate bowl, mix 2 cups of the flour, baking soda and salt. Stir to combine. Add this to the butter/cream mixture. Once incorporated, start adding flour 1/2 cup at a time, mixing well after each. Add until dough starts pulling away from the bowl.
Using a size 20 cookie scoop, place mounds onto prepared sheet. (I used a 20 scoop and got 22 cookies from the batch.) Bake for 8-10 minutes. DO NOT OVERBAKE. Cookies will be light-colored when done. Let cool on clean dry surface before icing.