In a large soup pot, bring 6-8 cups of water to boil. Once the water is boiling, add the chicken breasts, onion, bay leaves, and salt. Simmer for 20-25 minutes until the chicken reaches an internal temperature of 165°F. Remove chicken from the liquid and allow to cool for 15 minutes. With 2 forks, shred the chicken into thin pieces. Set aside until ready to use.
Melt butter in a large saucepan, over medium heat. Add the garlic and poblano peppers and sauté until softened, about 10 minutes. Sprinkle the flour over the veggies and cook for 1 to 2 minutes, stirring constantly to prevent any clumps. Stir in green chilies, chicken broth and milk. Using an immersion blender, puree the mixture until smooth. Bring the mixture to a simmer. Add the cilantro, cumin, and salt. Stir, and remove from the heat.
Preheat the oven to 375°F.
Coat the bottom of a 9×13″ baking dish with a light layer of the cream sauce. Place some shredded chicken and cheese on a tortilla, roll it up and place it in the baking dish, seam side down. Repeat with the rest of the tortillas, chicken, and cheese. Pour the sauce over the top of the tortillas in the baking dish. Sprinkle 1 cup of the shredded cheese in an even layer on top.
Bake the enchiladas, uncovered, for 15 to 20 minutes or until the cheese has melted and the sauce is bubbling. Squeeze lime juice over the top of the enchiladas and garnish with avocado, red pepper flakes and cilantro. Serve immediately.
