Preheat oven to 375 degrees F. In a large bowl, beat butter with sugar and brown sugar at medium speed until creamy and lightened in color (about 4 minutes). Add vanilla and egg, and mix on low speed until incorporated. Stir flour with baking soda, salt, and spices; add to creamed mixture, mixing well. Stir in oats. Fold in chocolate chips and walnuts. Drop by rounded tablespoon onto ungreased cookie sheets.
Bake 8 to 9 minutes for a chewy cookie, 10 to 11 minutes for a crisp cookie. Cool 1 minute on a cookie sheet; remove to wire cooling racks. Store in tightly covered container. Makes about 6 dozen 2-inch cookies.