I always start by roasting my hatch chiles under the broiler or on a hot grill until the skins blister and blacken all over. Once they're charred, I seal them in a bowl covered with plastic wrap for about ten minutes, which steams the skins loose. After that, I peel off the blackened skin, pull out the stems and seeds, and chop the flesh into small pieces for the filling and sauce.
In a large bowl, I combine the shredded chicken with half of the chopped hatch chiles, the diced onion, cumin, and a pinch of salt. I like to mix this well with a fork so every bite of filling gets some chile in it. If I'm using rotisserie chicken, I shred it while it's still warm since it pulls apart so much easier that way.
I melt the butter in a saucepan over medium heat, then whisk in the flour to form a paste and let it cook for about a minute. Slowly, I pour in the chicken broth while whisking constantly so no lumps form. Once it starts to thicken, I stir in the cream cheese, sour cream, and remaining hatch chiles until the sauce turns smooth and creamy.
I spread a thin layer of the hatch chile sauce across the bottom of my baking dish so the tortillas don't stick. Then I warm each tortilla for a few seconds so it stays pliable, spoon in the chicken filling along with a little cheese, roll it up snugly, and set it seam-side down in the dish. I repeat this until the pan is full.
Once all the enchiladas are rolled, I pour the remaining sauce evenly over the top and sprinkle on the rest of the cheese. I cover the dish with foil and bake at 375°F for about 20 minutes, then uncover it and bake for another 10 minutes so the cheese gets golden and bubbly on top.
I always let the enchiladas sit for about 5 minutes before serving, which helps the sauce set up so it doesn't run all over the plate. Right before serving, I scatter fresh chopped cilantro over the top for a bright, herby finish that balances the richness of the sauce