In a medium bowl with a handheld electric mixer or in the bowl of a stand mixer fitted with the paddle attachment, whip together the butter, powdered sugar, brown sugar, flour, salt, milk or cream, and vanilla, until very light and fluffy, 2-3 minutes.
Stir in the chocolate chips. Refrigerate until ready to serve; take the frosting out of the refrigerator about an hour before using so it can soften up a bit.
Notes
Browning the Flour: if you want to get completely gourmet and complex in the flavor department, try browning the flour before using in this recipe. It’s as simple as it sounds – throw the flour in an even layer in a skillet and, over medium heat, cook it, stirring often, until it’s golden. Let it cool and use it in this recipe and you’ll get cookie dough frosting with a deliciously nutty, almost browned-butter-like flavor.Raw Flour: for those of you concerned about eating raw flour, that simple step of browning the flour might be the key to having cookie dough frosting in your life.