In a bowl, cream butter and brown sugar until light and fluffy. Add eggs and vanilla; mix well. Combine oats, flour, baking soda and salt; add to the creamed mixture. Spread two-thirds into an ungreased 15x10x1-in. baking pan; set aside.
For filling, heat the milk, chocolate chips, butter and salt in a microwave-safe bowl until chips are melted. Remove from the heat; stir in walnuts and vanilla. Spread over top. Drop remaining oat mixture by tablespoonfuls over chocolate.
Bake at 350° for 20 to 25 minutes. Cool on a wire rack.