MIX 3 Tbsp. powdered sugar, 2 Tbsp. water and egg yolk in small saucepan until smooth. COOK over medium heat, stirring constantly, until mixture bubbles. REMOVE from heat; let cool 15 minutes.
BEAT butter in mixer bowl on high speed until smooth and creamy. ADD 1 cup powdered sugar, 2 Tbsp. water and the cooled egg yolk mixture. BEAT on medium speed until smooth.
GRADUALLY BEAT in remaining powdered sugar, adding up to 1 Tbsp. water as needed, 1 tsp. at a time, until frosting has a spreading consistency. ADD vanilla. BEAT on high speed until smooth, adding any remaining water, if needed.
Cooked yolk mixture must cool enough so it doesn’t melt the butter in Step 2.