Preheat oven to 350°. Line mini muffin pans with paper liners.
Place butter and 4 ounces white chocolate in a large bowl. Microwave on high in 30 second intervals, stirring between each, until mixture is smooth.
Stir in brown sugar and granulated sugar. Stir in eggs, one at a time, and beat well after each addition. Gradually stir in flour. Stir in vanilla. Then, stir in white chocolate morsels and nuts.
Spoon batter into muffin pans. Bake for about 15 minutes, until lightly browned. Cool in pans for 5 minutes. Then, remove from pans and cool on wire racks.
Makes about 60 blondies.