Using rotisserie chicken, shred to have at least 2 cups, save remaining for other use (depending on size of rotisserie chicken).
In a large Dutch oven over medium low heat melt the butter and sauté the onion and garlic with the cumin for several minutes.
Add the flour and stir to combine. We are making a roux, it should cook and turn a golden color on medium heat. Add the chicken stock and stir to make a thick paste. Next turn the heat to low and add the milk. Stir to incorporate completely. By adding the milk to the basic roux and chicken stock we have made a béchamel sauce.
Meanwhile in another large pot cook the pasta per package instructions. Drain and set aside, saving 1/4 cup of the pasta water.
Add the pasta water and cheese to the béchamel sauce and whisk to melt in. Next add the roasted green chilies.
Add the cooked pasta and chicken to the Dutch oven that has the green chili cheese sauce. Toss to coat evenly and serve.
Substitute canned chiles with 4 fresh seeded, roasted and chopped green chiles like Hatch, Anaheim or other mild green chile. Feel free to add a diced jalapeño for heat too, if you prefer.