Fully pre-heat your broiler.
Slice the stems off the three poblanos and one jalapeno and then cut the peppers in half vertically. Remove the seeds. Place the poblanos and jalapenos, skin side up on a foil-lined baking sheet. Broil until the skins have blackened.
Remove from the broiler to cool. Turn off the broiler and heat the oven to 350° F.
Place the spinach into a blender. When the peppers have cooled, remove the skins. Place two of the poblanos and the jalapeno into the blender. Cut the remaining poblano pepper into thin strips and reserve.
Heat the butter in a saucepan. Add the onion and on low to medium heat cook the onion until soft. Do not brown the onion.
Add the garlic when the onion is almost done.
Add the flour and cook an additional minute or two. Slowly whisk in the milk and chicken broth and continue to cook and whisk until the sauce thickens, about five minutes. Season with salt and pepper.
Pour the mixture into the blender with the spinach and chiles. Allow it to cool somewhat and then blend it. Reserve the sauce in the blender.
Butterfly the two chicken breasts by cutting them down the center parallel to the cutting board. Season both sides of the breasts with salt and pepper.
Heat some vegetable oil in a large skillet until it starts to smoke. Sear the first side of the chicken until fully browned, flip and sear the other side.
Remove the breasts and cut into thin strips. Don’t worry if they’re not cooked through to the center as they will be added back to the pan to cook more.
Reheat the pan, adding more oil if necessary. Return the chicken to the pan as well as the one reserved poblano that was cut into strips.
Add the chili powder and cumin. Sauté a few minutes until the chicken is fully cooked and the poblano has softened.