Always cook turkey to an internal temperature of 165 degrees F.
In a medium bowl, combine the mirin, soy sauce, honey, ginger, and garlic. Reserve ¼ cup of the mixture for a later use. Add the turkey to the remaining mixture, and stir to coat. Marinate at least 1 hour or up to overnight, if time permits.
Remove the turkey from the marinade, discarding the marinade. Thread pieces of turkey, peppers, and green onions onto skewers.
Preheat a grill over medium heat.
Cook the skewers on the grill, 18 to 20 minutes, turning the skewers a quarter turn every 3 minutes. In the last 5 minutes of cooking, brush the reserved ¼ cup marinade on the kebobs. Always cook turkey until well done, or an internal temperature of 165 degrees F as measured by a meat thermometer.