Preheat the oven to 350ºF (175ºC) and spray a 9×13-inch baking dish with cooking spray.
Cook the penne according to package directions until al dente, drain well, and set aside.
In a small saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1 minute to form a roux.
Slowly whisk in the chicken broth, then add garlic powder, onion powder, and southwestern (or taco) seasoning. Cook, whisking, until the sauce is smooth and starts to thicken.
Remove the sauce from the heat and stir in the sour cream and the diced green chiles until combined.
In a large bowl, toss the cooked pasta with the sauce, chopped cooked chicken, and half of the shredded Monterey Jack cheese.
Transfer the mixture to the prepared baking dish, sprinkle the remaining cheese on top, and spread evenly.
Bake for 25–30 minutes, until the casserole is bubbly and the cheese is melted and lightly browned.