We approach a problem of motion planning and stabilization for a benchmark example, known as the “Butterfly” robot. It was proposed as a benchmark challenge for developing systematic techniques for nonprehensile rolling manipulation. A dynamical model of the underactuated system with a non-unilateral contact is derived. The recently proposed methodologies, known as virtual-holonomic-constraints-based motion planning and transverse-linearization-based orbital stabilization, are appropriately extended to suit the task. Finally, the feasibility is demonstrated through a hardware implementation and an experimental validation of the concept.