Heat oven to 325°. Place paper liners in cups of mini muffin pans (36 total).
In a small bowl, whisk together flour, baking powder and salt. In a large bowl, beat butter until smooth. Add sugar and beat until fluffy, about 2 minutes. Add egg whites, one at a time, beating well after each. Beat in vanilla. On low, beat in half the flour mixture, then 3/4 cup water. Beat in remaining flour mixture.
Divide batter evenly among prepared cups. Bake at 325° for 18 minutes. Frost and decorate as desired.