2 small fresh Serrano chiles, coarsely chopped, including seeds
2 small garlic cloves peeled
½ teaspoon aniseed
2 tablespoons mild olive oil or vegetable oil
½ cup poached chicken, including 4 to 5 cups of chicken stock
1 small avocado leaf
4 Avocados from Mexico peeled, pitted and diced
Put the chicken pieces in an 8-quart pot with the water, carrots, celery, onion, parsley, bay leaf and 1 tsp salt. Bring the water to a simmer over high heat, skimming any foam from the surface as necessary. Reduce the heat and simmer until the chicken is just cooked through, about 30 minutes.
Remove the chicken pieces from the stock. When they’re cool enough to handle, remove the skin from the chicken, if desired. Strain the stock into a wide bowl, discarding the vegetables and herbs.
You can keep the chicken in the stock and refrigerate it up to two days. You can also separate the two and keep the stock in the refrigerator for up to five days, or in the freezer for three months. Be sure to let the meat and stock cool uncovered first.
For the pistachio sauce, turn 1 or 2 burners on the stove to high and roast the poblano chiles on the racks of the burners (or directly on the element of an electric stove), turning frequently with tongs, until they are blistered and charred all over, 4 to 6 minutes. Put the poblanos in a bowl and cover with a plate to sweat, 15 to 20 minutes.
Rub off the skin from the poblano chiles with a paper towel or your fingers, then cut them open lengthwise. Cut out the seed pods, veins, and stems, and lay the chiles flat. Wipe the chiles clean of seeds, discard the seeds, and tear the chiles into large pieces.
Heat a small heavy skillet over medium heat and toast the sesame seeds and chile seeds, stirring and tossing constantly, until they’re fragrant and a shade darker, about 4 minutes.
Transfer the poblanos and toasted seeds to a blender. Add the pistachios, serrano chiles, garlic, ¾ salt, aniseed, and 2 cups of the chicken stock, and blend until very smooth, about 3 minutes.
Heat the oil in a 4- to 5-quart heavy pot (this will give you enough room to add the chicken later; if you’re making just the sauce, a 3- to 4-quart pot is fine) over medium heat, then add the blended mixture and simmer, stirring frequently, until it has thickened slightly, about 5 minutes. As it’s simmering, swish a little liquid around the blender and add it to the pot.
Reduce the heat to low and simmer the sauce, uncovered (use a splatter screen so the sauce doesn’t make a mess of the stove), stirring frequently, until small pools of oil appear on the surface of the sauce, about 45 minutes. As the sauce simmers, add more stock, as necessary, to maintain a velvety consistency that thickly coats a wooden spoon, but isn’t gloppy.
Heat a comal, griddle, or heavy skillet over medium-low heat, and toast the avocado leaf, turning it frequently with tongs, until fragrant and lightly browned, 1 to 2 minutes. Crumble the leaf into the blender. Add 1 cup of the sauce, and blend until smooth. Return the mixture to the remaining sauce in the pot and cook for 5 minutes more. Season to taste with additional salt.
Add the chicken to the sauce, reduce the heat to low, and cook until it’s just heated through, 15 to 20 minutes. Top with diced avocados.