Preheat oven to 325°. In a large bowl, beat together the butter, the granulated sugar and the dark brown sugar with an electric mixer until light and creamy, about 3 minutes. Beat in the vanilla and the eggs until smooth.
In a medium bowl, combine the flour, baking soda and salt. Gradually beat the flour mixture into the butter. Mix in the chocolate chips and nuts.
Using a small ice cream scoop or a ¼ cup measure, drop the batter onto greased cookie sheets, allowing 3 inches in between each one for spreading. Bake for about 10 minutes, or until light golden brown. Let cool on the baking sheet before removing to a rack to cool completely.