Preheat oven to 350°F (175°C). Line mini muffin pans with paper liners.
Place the butter and chopped white chocolate in a large bowl. Microwave on half power in 30 second intervals, stirring between each, until the mixture is smooth. Let cool slightly.
Stir in the brown sugar and granulated sugar. Stir in the eggs, one at a time, and beat well after each addition. Stir in the vanilla.
Gradually stir in the flour, mixing just until combined.. Then, stir in white chocolate morsels and nuts.
Divide the batter among the prepared muffin cups. Bake for 15 minutes, or until lightly browned.
Cool in the pans for 5 minutes. Then, remove from the pans to a wire rack to cool completely.
Notes
Store in an airtight container at room temperature up to 3 days.