1. Position rack in middle of oven. Heat oven to 325 degrees F. Line 9 x 9 x 2-inch square baking pan with foil; grease.
2. In metal bowl set over saucepan of barely simmering water, melt white chocolate and butter, stirring until smooth. Let cool to room temperature.
3. In large bowl, beat eggs, sugar, vanilla on medium speed until thickened and pale, 3 minutes. On low, gradually beat in chocolate mixture. Into a bowl, sift flour, baking powder, salt. Beat into chocolate mixture until combined. Spread evenly in prepared pan. Sprinkle with berries.
4. Bake in middle of 325 degrees F oven until top is very lightly browned but center still soft when lightly pressed, 45 to 50 minutes. Let cool completely in pan on rack.