Preheat oven to 375 degrees.
Cream butter, sugar, brown sugar, and vanilla in a large bowl until fluffily.
Add eggs, beat well.
Gradually add flour to creamed mixture and beat well.
Stir in chocolate chips and nuts (optional).
Drop by teaspoonfuls onto greased cookie sheet.
Bake at 375 for 9-10 minutes, or until lightly browned.
Cool for 5 minutes, then transfer cookies to wire cooling rack.