Heat oven to 350°F. Combine powdered sugar, butter, egg and vanilla in large bowl. Beat at medium speed, scraping bowl often, until light and fluffy (2 to 3 minutes). Reduce speed to low. Add flour; beat until well mixed (1 to 2 minutes).
Shape rounded teaspoonfuls of dough into 1-inch balls. Beat egg yolks and water with fork until well mixed in small bowl. Dip balls of dough into beaten egg yolks, then into peanuts. Place onto ungreased cookie sheets.
Bake for 12 to 16 minutes or until top springs back when touched lightly in center.