In a medium size sauce pot, add ingredients from apple juice to scallions, if using. Simmer the sauce over medium-low heat and stir with a wooden spoon until the sauce simmers and starts bubbling, about 6-8 minutes.
In a small bowl stir-well arrowroot with water. Slowly drizzle it into the sauce until it thickens, about 30 seconds to 1 minute.
Off heat, let it cool before storing it in a glass container. Store it in the fridge. Best finish in 2 weeks.
Taste and make seasoning adjustments to your own liking, particularly the vinegar quantity. Apple cider vinegar is more acidic (and less sweet) than rice vinegar.
If you want to avoid the arrowroot starch, the basic teriyaki sauce in Japan is made without the starch. Simply simmer the sauce longer over medium-low to low heat for 12-15 minutes.
The very basic Paleo teriyaki sauce has no garlic, ginger, and scallions. Feel free to try this version if it works better for your needs. :)