Whisk soy sauce, mirin, brown sugar, sesame oil, ginger and garlic together in a small saucepan over medium heat. Bring to a boil then reduce to a simmer for about 5 minutes. Let cool slightly.
Add ¾ of the sauce to a sealable zip lock bag. Add the salmon and make sure the filets are covered in marinade. Set aside for 30 minutes at room temperature.
Pour the remaining ¼ marinade into a small serving bowl to be used as a drizzle on the final dish.
Preheat air fryer to 390 degrees. Or preheat your grill to high heat and clean and oil the grates.
Wipe or spray your air fryer basket with high heat cooking oil.
Remove filets from marinade (discard marinade). Shake off any excess marinade. Place fish in air fryer, making sure not to have the filets touching each other. Or, place fish on foil, then onto the grill (reduce grill heat to medium).
Cook salmon for 5-6 minutes, or until desired doneness. Cooking time will vary depending on the thickness of your salmon filets and the variation in air fryers. Safe internal temperature for salmon is 145 degrees, but pull out of air fryer at 140, as the temperature will continue to rise. Or, if you prefer your salmon rosy in the center, pull it out at 125-130, as measured in the thickest part of the filet. If you are grilling, time will be closer to 8-10 minutes, depending on filet thickness. No need to flip the salmon with either cooking method.
Assemble bowls by dividing rice among 4 bowls. Add salmon, cucumber, edamame, avocado, seaweed salad, scallions and pickled ginger equally to the bowls.
Sprinkle bowls with black sesame seeds. Serve with lime wedges and reserved teriyaki sauce.