In a crockpot or in a baking dish, add the chicken breasts and half of the green chiles. Cook on low in the crockpot for 1-2 hours until tender, or bake at 400 for 15-20 minutes until the internal temperature reads 165 degrees. Shred and set aside.
In a small pot, boil water for the noodles. When the water is boiling, add the elbow noodles and boil until they are al dente. Reserve 1-2 tablespoon of the pasta water on the side, then drain the noodles.
In a medium saute pan over medium heat, add the butter and heat until melted.
Add the flour to the pan and whisk to combine into a paste. Cook for 30 seconds.
While whisking constantly, slowly pour in some of the milk. The paste will continue to thicken as more milk is added. Continue whisking until all the milk has been added.
Season the roux with salt and pepper, then add the shredded cheeses. Whisk until the cheese has melted. Then let the sauce bubble over the heat for 1-2 minutes. Remove from the heat and set aside.
Add the noodles to the pan with the cheese sauce and mix to combine. Add the other half of the green chiles can and mix.
Finally, add the shredded chicken to the macaroni and cheese and mix well. Set aside.
Heat a separate pan over medium heat. While the pan is heating, slice your bread 1 inch thick and butter one side. When the pan is hot, place one slice of bread butter side down. Depening on the size of your bread, add about ⅓ cup of the macaroni mixture on top of the bread. Place the other half of the bread on top, butter side up.
Toast the grilled cheese for 2-3 minutes on one side, then very carefully flip the grilled cheese with a spatula. Toast for another 1-2 minutes or until golden brown.