Preheat the oven to 350 degrees F (or 325 degrees F for convection bake) and line several half sheet pans with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment (or in a bowl using a handheld electric mixer), add the butter, oil, granulated sugar and powdered sugar. Sprinkle the baking soda, cream of tartar, and salt across the top of the sugars (don't add the baking soda and cream of tartar in one lump or it might clump while mixing). Mix until well-combined and super creamy, 1-2 minutes, scraping down the sides of the bowl as needed.
Add the sour cream, eggs and vanilla and mix until well-combined, 1-2 minutes, again scraping down the sides of the bowl as needed.
Add the flour and mix until no dry streaks remain and the mixture is evenly combined; don't overmix.
Scoop the dough into about 3-tablespoon sized portions (I use a #20 cookie scoop) and roll into balls. Place several inches apart on the prepared baking sheets. Add about 1/2 cup granulated sugar to a shallow dish or bowl. Lightly spray the bottom of a flat-bottomed glass with cooking spray and dip the bottom of the glass into the sugar. Press each cookie into an even thickness dipping the bottom of the glass into the sugar between each press (no need to spray it again with cooking spray after the first time). The edges of the cookie will ruffle out a bit. It's really up to you how thick or thin to press the cookies. I like them between 1/4- and 1/2-inch thick.
Bake the cookies for 7-9 minutes until the edges are set (it's ok if the center of the cookies looks slightly under baked).
Let the cookies cool for a few minutes on the baking sheets before removing to a cooling rack to cool completely.
For the frosting, in a medium bowl (can use a handheld or stand mixer) combine the butter, sour cream and vanilla. Mix until thick and smooth and creamy, 1-2 minutes. Add the powdered sugar and cream (or milk) and mix until well-combined and creamy, scraping down the sides of the bowl as needed. Add additional cream, if needed, to adjust the consistency of the frosting so it is thick but still soft and spreadable.
Frost the cooled cookies and decorate with sprinkles, if desired.
Vanilla Flavor: I've also used vanilla butter emulsion in place of the vanilla extract (in both the cookies and frosting) for a super yummy, buttery vanilla flavor.Overflouring: be careful not to overflour the dough or the cookies might be dry instead of soft after baking. If you don't weigh your ingredients, make sure to fluff the flour in the container before scooping in the measuring cup and leveling (don't pack or shake the flour into the cup!).Make-Ahead: these cookies do amazingly well baked, frosted, sprinkled and frozen. Once frosted, I place them in a single layer on a baking tray, freeze, and then slide them into a tupperware container or ziploc bag (and separate layers with pieces of parchment or wax paper). They thaw great and taste amazing.