1. Heat oven to 375 degrees F. Combine flour, oats, baking soda, and salt in a medium bowl with a whisk.
2. Soften butter with a rolling pin. Beat butter and sugars in large mixer bowl at medium speed until creamy, 2 minutes. Add eggs one at a time, beating well after each addition. Beat in vanilla. At low speed, gradually beat in flour mixture until blended. Stir in chips and nuts.
3. Drop dough by heaping tablespoonfuls 2 inches apart on 2 large ungreased cookie sheets. Bake 13 to 14 minutes, until golden brown. Let cookies stand on sheets 2 minutes, then transfer to wire rack to let cool completely. Repeat. Makes about 45 cookies.