For the blueberry reduction, combine blueberries and water in a blender or food processor and blend until smooth. Pour into a small saucepan and cook over medium low heat, stirring occasionally, until it has thickened, about 30 minutes. You want it to be thick but still syrupy, somewhere between juice and jelly. Cool for at least 15 minutes before using in cupcake batter and completely before in frosting. Extra reduction can be used to drizzle on cupcakes or poured over things such as pancakes and waffles.
For the frosting, in bowl of stand mixer fitted with whisk attachment, cream butter with 1 cup powdered sugar. Add blueberry, vanilla, cocoa, and salt and mix until smooth. Add remaining powdered sugar a little at a time until fully incorporated. Beat on high speed for about 1 minute until light and fluffy.