Cream the butter and both sugars in a large bowl. Beat with electric mixer until smooth. Add the egg, egg whites, salt and the vanilla. Beat well.
In a smaller bowl, combine the dry ingredients (flour, ground oatmeal and baking soda). Slowly add the dry items into the larger bowl and beat with electric mixer until batter is smooth and creamy. Fold in entire bag of chocolate chips, and if you like add the walnuts.
Drop dough by large teaspoons (or scant Tablespoons) onto cookie sheet and bake for 11 minutes (the time REALLY depends on your oven so watch that first batch!).