Combine first 3 ingredients in a medium bowl; add butter and vanilla, and beat at low speed with an electric mixer until blended. Stir in 1 cup chocolate morsels.
Press dough into an ungreased 9-inch square pan; prick dough with a fork.
Bake at 325° for 20 minutes or until lightly browned. Sprinkle remaining 1 cup morsels over top, and spread to cover. Cut shortbread into 25 (about 1 3/4-inch) squares; cut each square into 2 triangles. Let cool 30 minutes in pan before removing. Serve with ice cream, if desired.