Feel free to cook the chicken however you want. I go back and forth between poaching it and the brine-and-bake method.
To poach the chicken, cover the chicken breast with water in a saucepan and bring it to a boil. Add a half onion, cilantro sprigs and a pinch of salt for additional flavor. Once boiling, reduce heat and let simmer for 20 minutes or until the chicken is cooked through. Once cooked, set aside to cool.
To brine-and-bake the chicken, add 1/4 cup salt to a quart of water in a mixing bowl. Dissolve the salt and add the chicken, letting it brine covered in the fridge for 30 minutes or so. If the chicken isn't fully submerged then add a bit more water. Once brined, pat dry the chicken and add it to a baking sheet. Bake in the oven at 400F for 20 minutes or until the chicken is cooked through and no longer pink inside (160F).
Meanwhile, de-husk and rinse the tomatillos. I usually de-stem them as well. Roast the tomatillos and poblano in the oven at 400F for around 25-30 minutes.
Cut off the stem and de-seed the roasted poblano. You can also remove any loose bits of skin. Add it to a blender along with the tomatillos, 1/2 onion, 2 garlic cloves, 10-12 sprigs of cilantro, and 1/2 of a jalapeno pepper. Pulse blend and taste for heat level, adding the other half of the jalapeno if you want more heat.
Heat a glug of oil in a saucepan over medium heat. Add the green sauce from the blender and simmer for a few minutes. Add 1 cup chicken stock and 1/4 cup heavy cream to the mixture. Cook on medium-low until heated through.
Use two forks to shred the chicken and add it to a mixing bowl along with 2-3 tablespoons finely chopped onion, a handful of cheese, and dashes of salt. You can also add some green sauce if you want.
Heat the corn tortillas in the oven for a few minutes. (Or nuke them in some damp paper towels for 60 seconds.)
Prepare the baking dish by adding a few spoonfuls of the green sauce to prevent sticking.
On a plate, add a couple spoonfuls of the green sauce. Dredge a tortilla in the sauce, flip, and fill with a small handful of the chicken mixture. You can optionally add more cheese on top. Roll up and place seam side down on the baking dish. Keep going ‘til the chicken is gone. Add the remaining sauce on top of the enchiladas along with a final layer of cheese.
Bake for 10-15 minutes or until the cheese is melted.
Serve immediately. You can optionally garnish with freshly chopped cilantro.