1. Preheat oven to 350°. Butter a 15- x 10-inch jelly-roll pan.
2. Bake walnuts at 350° in a single layer in a shallow pan 8 to 10 minutes or until toasted and fragrant, stirring halfway through. Let cool 30 minutes.
3. Melt 1 1/4 cups butter in a 3 1/2-qt. heavy saucepan over medium heat; stir in granulated sugar, next 5 ingredients, and 1/3 cup water. Cook, stirring constantly, until a candy thermometer registers 290° (soft crack stage), about 20 minutes. Remove pan from heat, and stir in walnuts. Quickly pour mixture into prepared pan, and spread into an even layer. Immediately sprinkle milk chocolate and white chocolate morsels over top; let stand 5 minutes. Swirl chocolate using an off-set spatula. Cover and chill until firm (about 1 hour). Break toffee into pieces. Store in an airtight container in refrigerator up to 7 days. Serve cold or at room temperature.