1cupunsalted buttersoftened to cool room temp (still cool to the touch)
3cupspowdered sugar*sifted if lumpy
1tablespoonhalf and half or milk*plus more as needed
1 ¾teaspoonspure vanilla extract
Sugar cookie frosting:
Using a hand mixer, or stand mixer fitted with the paddle attachment, beat butter and half of the powdered sugar until well-combined (starting out the mixer low and increasing to medium-high). Slowly add the remaining powdered sugar (while beating), followed by extracts, pinch of salt, and 1 tablespoon milk. Continue to add more milk, a little bit at a time, until you get a creamy spreadable frosting. If desired, you can add food coloring at this point.
Turn the mixer to medium-high and beat well. Depending on how thick you want the frosting, you can easily adjust the consistency by adding more powdered sugar (to thicken) or more milk (to thin).
Frosting to spread or pipe:
Use a piping bag, small knife, or spreader to add the frosting to baked and cooled sugar cookies. Immediately top with sprinkles, if using.
Melted dippable frosting:
Prepare the frosting above adding extra powdered sugar and milk (see note).
Working with half of the frosting at a time: Place frosting in a wide shallow bowl and microwave for 15-20 seconds. Stir really well. The frosting should be melty and thin. Microwave for a few more seconds, and add a splash of milk, if necessary, to get it thin enough.
Working quickly, dip each sugar cookie face down into the frosting. Move the cookie around a bit, then flip it over and jiggle it back and forth to get the frosting to settle into an even layer. Top with sprinkles, if using, then set aside to allow the frosting to set.
Note: The frosting will firm up as it cools, so you might need to microwave it again to thin it out. Once you have used the first half of the frosting, proceed with microwaving the second half.
*For melted dippable buttercream: add an additional cup of powdered sugar and increase the milk to 3 tablespoons (plus more, as needed).