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. Bake until golden brown, about 15 mins. Cool cookies on sheets for 5 mins.
Transfer cookies to rack to cool.
This makes about 18. Don't let the cookies get too brown. They should still be very soft when removed from oven. Cream butter and sugar in a large mixing bowl. Add eggs one at a time.