Place a fine-mesh strainer over a small bowl. Place the yogurt in the strainer. Wrap with plastic wrap and place in the fridge to drain for at least two hours and preferably overnight. This step is important. Otherwise, the yogurt will be too liquid to make a proper frosting.
Using an electric hand mixer set on medium speed, beat together the strained yogurt, vanilla, and sweetener (and coconut flour if using) until the frosting thickens, about 2 minutes.
Cover and place in the fridge for 30-60 minutes while you bake and cool your cake or cupcakes.
To frost your cupcakes, wait until they are completely cool. Then fill a quart-size Ziploc bag with the frosting, snip the corner and use it to pipe frosting onto the cupcakes. Or simply use a spatula or a spoon to spread the frosting on the cupcakes.
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Notes
The sugar-free option has 37 calories and 1 gram of carbs per serving (this excludes the carbs found in sugar alcohols such as erythritol). This recipe makes enough frosting for 12 cupcakes. The nutrition info is for 1/12 recipe - the frosting needed for one cupcake, which is about 2 tablespoons. I don't recommend storing leftovers of this frosting or making it ahead of time. You should use it right away for cakes or cupcakes that would be enjoyed within an hour or so.