Preheat oven to 375 degrees. Blend butter, sugars, egg, and vanilla until fluffy, stopping once to scrape down sides of bowl, about 1 minute. Add flour, baking soda and salt and mix until just combined. Do not overmix. Stir in white chocolate chunks and nuts. Mound dough by 1/3 cupfuls onto lightly greased cookie sheet. Space about 2 inches apart. Bake at 375 degrees until lightly brown around edges, about 15 minutes. Cool on cookie sheet for 3 minutes, then remove to racks and cool completely. Store in air-tight container. Can be prepared ahead, store cookies up to 4 days at room temperature or freeze 3 weeks.