Use back of spoon to pack ice cream into foil-lined 1-1/2-qt. bowl. Crush 4 sugar cones; sprinkle over ice cream. Press gently into ice cream to form even crust.
Freeze 4 hours or until ice cream is firm.
Unmold dessert onto plate; remove foil. Break remaining cones into pieces; press into side of dessert.
Melt chocolate as directed on package just before serving dessert. Stir in oil; cool slightly.
