How can I speed recovery from broken mandible bone?

Depends on fracture. Some mandible fractures need surgery and some don't. Most require at least some period of immobilization either with wires or elastic bands. Maintain good nutrition during healing with protein shakes or supplements. Avoid eating hard foods once you can open your mouth.
P/ Mandible Fracture. The body tends to recover in a predictable timeframe. For instance, if you have a cut in your skin, it takes about 7 days for the edges to seal together. To keep your mandible intact, follow your oral surgeon, ent, or reconstructive surgeons instructions. Did you have surgery? Usually you take medication for pain, and a soft diet. If you have on-going or worsening pain, get seen asap.