Preheat your oven to 375˚F.

In a large pan/skillet heat up about 1 tablespoon of oil, add in your chopped poblanos stirring occasionally until they start to become tender.

Add in butter, once melted add garlic and cook for about 1 minute until the garlic becomes fragrant. Whisk in the flour until it is combined and allow to cook for another minute or two. Whisk in the chicken broth and milk until combined. Allow to simmer for a couple of minutes to allow the sauce to thicken up. Remove from heat, add in cilantro, and salt to taste. Take about 1/2 Cup of the sauce and mix it in with the shredded chicken.

Pour about half of the remaining sauce into the bottom of a baking dish. Spoon the chicken equally into the tortillas, roll the tortialls up and place them seam down in the backing dish. Pour the remaining sauce over the top of enchiladas, top with shredded cheese and back for about 20 minutes, until cheese is metler and getting some nice color.