Preheat oven to 350°. Lightly grease or paper-line 36 small muffin cups (13/4 inches in diameter).
Beat butter, sugars, egg, and vanilla in large bowl until fluffy. Stir together dry ingredients; gradually blend into butter mixture. Add milk; stir until blended. Stir in cranberries, walnuts and 2/3 cup white chips. Fill muffin cups almost full with batter.
Bake 18 to 20 minutes or until a toothpick inserted in center of muffin comes out clean. Cool five minutes and remove from pan to a wire rack. Cool completely.
Place remaining 1 cup white chocolate chips in small microwave bowl and sprinkle 2 tablespoons vegetable oil over chips. Microwave on high for 30 seconds or just until chips are melted when stirred.