In a large bowl, beat butter and sugars until blended. Beat in eggs and vanilla. In a small bowl, whisk flour, baking soda and salt; gradually beat into butter mixture. Stir in chocolate chips and walnuts.
Shape 1/4 cupfuls of dough into balls. Flatten each to 3/4-in. thickness (2-1/2-in. diameter), smoothing edges as necessary. Place in an airtight container, separating layers with waxed paper or parchment; refrigerate, covered, overnight.
To bake, place dough portions 2 in. apart on parchment-lined baking sheets; let stand at room temperature 30 minutes before baking. Preheat oven to 400°.
Bake until edges are golden brown (centers will be light), 10-12 minutes. Cool on pans 2 minutes. Remove to wire racks to cool.