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Preheat oven to 325 degrees F. Line cookie sheets with parchment paper.
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Cream butter, brown sugar and white sugar together in a large bowl. Add eggs one at a time, mixing thoroughly after each egg is added. Add vanilla. (I used my Kitchen Aid standing mixer with its paddle attachment for this step.)
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In a separate bowl, whisk flour, baking soda, cinnamon, and salt together. Add this dry mixture gradually to the butter/egg mixture. Add oats and walnuts. Mix until just blended.
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Drop heaping teaspoonfuls of cookie dough onto the cookie sheets. Allow two inches between each cookie to allow the cookies to spread while cooking.
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Bake at 325 degrees F. for fifteen minutes or until cookies are beginning to turn a light brown and are firming up. Remove from oven and cool on a rack.