What should I eat in order to promote my broken humerous to heal?

Well-rounded diet. Nothing extraordinary is warrented. A well-rounded healthy diet will support strong bone healing.
Balanced diet. A balanced diet will promote your overall health. Make sure you have a calcium intake of 1000 mg day through food or supplements. Supplemental vitamin d (up to 2000 iu/day) may help if you like many have low vitamin d. Discuss with a dietitian to get personalized recommendations. Depending on how fracture happened you may want to consider asking your doctor about getting a bone density test.