Add the mirin, ginger, honey and soy sauce to a small sauce pan and bring to a boil. Remove from heat and whisk in miso, then add onions and 1 TBS sesame oil. Allow to cool below 40 degrees before marinating steak.
Place flank steak in a resealable bag and pour marinade over, then press out air and refrigerate for a minimum of 4 hours, up to 24 hours.
Remove steak from marinade, allow to sit out for 30 minutes, then grill. Cook until medium or medium rare, about 5-6 minutes per side. Remove from grill and allow to rest for 5 minutes before slicing.
Slice AGAINST the grain, and serve with sautéed shishitos and shiitakes, and some cooked brown rice.