Mix all ingredients, except orange slices, in a small bowl. Set aside 1/3 cup of the marinade and leave at room temperature.
Place steaks in a zip top bag and pour remaining marinade over them. Add in orange slices, remove as much air as possible, and place bag on a plate (in case of leaks). Place in refrigerator for at least 4 hours to overnight.
Remove steak from marinade, discard marinade that’s been in contact with the raw meat and blot steaks dry with a paper towel. The steaks will be a deep brown color at this point. Allow steaks to come up to room temperature for about an hour. While steaks are coming up to temp, light grill and set for maximum direct heat. Allow gas grill to preheat for at least 15 minutes. For charcoal grill, be sure coals are piled high and as close to grilling grate as possible.
Place steaks over direct heat, flipping them every 20 seconds. Using a reliable quick-read thermometer, start checking internal meat temperature after about 3–4 minutes of grilling. When meat temperature reaches about 100°F, start basting the steaks with the reserved marinade before every flip.
When steak temperature reaches 120°F remove from grill, tent with aluminum foil and allow to rest for 5–6 minutes. Because we grilled these steaks with intense direct heat, the energy created is going to induce carry-over cooking for several minutes after the steaks have been removed from the grill. After a 5-minute rest, the steaks will be at a perfect medium rare range of about 127° or so.
Slice, garnish, and serve. Feel free to season with salt and pepper but go easy. The tamari, while not as salty as soy sauce, is still a bit salty so be sure you taste before seasoning.
For this recipe, I'm using strip steaks from Omaha Steaks, but feel free to use it on top sirloin, flank steak, or even ribeye. I've been getting meats from Omaha Steaks for a long time and honestly you can't go wrong with anything from them. If you don't have the time to create your own meals, they also have entire prepackaged meals which are excellent and save a ton of time.