Place the whole chicken, including giblets if you have them, in a large stockpot along with the scallions, leeks, garlic, black peppercorns, and 2 teaspoons salt. Fill the pot up with water until it's just covering the chicken.
Place the pot on the stove over high heat and bring to a boil. Reduce heat and simmer for 1 hour 30 minutes, skimming the fat from the surface of the liquid periodically. Turn the heat to medium-high and cook over a low boil for an additional 30 minutes. Turn off the heat.
Using kitchen tongs, scoop out the chicken and transfer it to a bowl. Pour the remaining stock through a sieve into a large bowl. Discard the solids. Wipe out the pot and return it back to the stove.
Carefully peel the chicken and discard the skin. Pick the meat from the bones and set it aside. Discard the carcass or reserve for another batch of stock, if desired.