Preheat oven to 350 F. Grease 2 heavy large cookie sheets. Mix first 4 ingredients together in a small bowl. Using an electric mixer, beat butter, sugar and vanilla in a large bowl until light and fluffy. Beat in egg. Stir in dry ingredients, then vanilla milk chips and nuts. Drop cookie dough by scant 1/4 cupfuls onto prpared cookie sheets, spacing evenly. Bake until golden brown, about 15 mins. Cool cookies on sheets for 5 mins. Transfer cookies to rack to cool. This makes about 18.
This recipe from the Regent Beverly Wilshire Hotel in L.A. Tips: Don't let the cookies get too brown. They should still be very soft when removed from oven. And for those of you who didn't know: Nestles now makes vanilla milk chips along with their chocolate and butterscotch.