Roast the chicken legs, green onions, carrots, and onions in a tray at 425 ℉/220 ℃ for 40-60 minutes or until deep dark brown but not burnt.
Add the roast chicken, veggies, and the rest of the ingredients to the Instant Pot (except for the lime and xanthan gum).
Fill to the max line with cold water and turn on the sauté function for 25 minutes. Let it come to a boil.
Skim the stock of any impurities or foam as it comes to a boil.
Once boiled, turn off the heat. Double-check that the water is not filled past the max line. Close the lid and set on high pressure for 2 hours.
Naturally release the pressure for 10 minutes. Manually release the rest.
Open the lid and skim off any fat from the top. Strain through a fine-mesh strainer.
Pass the black garlic through a tamis or mesh strainer to remove the skin. Add this, the xanthan gum and the fresh lime juice to the strained broth. Blend with an immersion blender. Check the seasoning and serve with freshly chopped green onions and some of the cooked chicken meat if desired.