Prepare poaching liquid. Cut onion in half. Thinly slice half of the onion, set the other half aside. Peel and thinly slice 3 of the garlic cloves. Place sliced onion and sliced garlic in a large (4 quart) saucepan along with 2 teaspoons of the salt and the 4 cups of water. Bring to a boil over medium-high heat.

Poach chicken. Add chicken and return to a simmer. Lower heat so liquid is gently simmering. Cook, uncovered, until cooked through, about 25-30 minutes.

Char veggies for salsa. Heat broiler to high and arrange rack to the top. Cut other onion half into half again. Place onion, remaining 2 garlic cloves (unpeeled), tomatillos, and jalapeños on a baking sheet. Place under broiler and broil, turning once or twice, until charred on all sides, about 20 minutes. Remove garlic once it is golden and continue broiling the other vegetables until charred.

Blend sauce. Peel garlic and remove stems from jalapeños. Also remove jalapeño seeds if you are sensitive to heat. Let vegetables cool slightly then place charred tomatillos, garlic, jalapeno, and onion in a blender. Add cilantro and salt and blend on high until smooth.

Shred chicken. Once chicken is cooked through, drain through a fine mesh sieve into a heatproof bowl. Save cooking liquid to use as chicken broth in a soup or sauce. Let chicken cool then shred into bite-sized pieces.

Toss with sauce. Add chicken and the onions and garlic it cooked with back in the saucepan. Add salsa verde and heat over medium until the flavors have melded and it is warmed through, about 5-10 minutes. Taste and season with salt as needed.

Serve. Serve in warm tortillas as tacos topped with avocado slices or in a burrito bowl or flautas.