Stir together brown sugar, butter, and corn syrup in a large saucepan; cook over medium heat until sugar dissolves and butter melts. Remove from heat. Stir in 1/4 cup peanut butter and vanilla. Gently stir in oats. Press into bottom of an ungreased 13" x 9" pan lined with aluminum foil. Bake at 375° for 20 to 22 minutes or until browned.
Melt together chocolate morsels, butterscotch morsels, and shortening in a saucepan over medium heat, stirring until smooth; stir in 1/2 cup peanut butter. Spread over baked cookie crust; sprinkle with peanuts. Let cool in pan on a wire rack 20 minutes. Cover and chill 2 to 3 hours or until firm. (Or pop them in the freezer to speed cooling. Just be sure to let them stand 5 minutes at room temperature before cutting.)
Lift uncut cookies out of pan using foil as handles. Cut crosswise into approximately 1"-thick sticks using a large chef's knife. Wrap in cellophane bags or plastic wrap for gift giving.