Begin by boiling a large pot of salted water. Once boiling, add the angel hair pasta and cook according to package instructions until al dente. Drain the pasta and set it aside.
In a large skillet, heat 1 tablespoon of olive oil and 1 tablespoon of butter over medium heat. Add the diced onion and sauté for 3-4 minutes until it becomes translucent. Stir in the green chilies and cook for an additional minute.
Sprinkle in 2 tablespoons of all-purpose flour and stir to combine, cooking for about 1 minute to remove the raw flour taste. Gradually whisk in 2 cups of chicken broth, ensuring there are no lumps. Bring the mixture to a gentle simmer.
While the sauce is simmering, cut the chicken breasts into bite-sized pieces. Add the cooked chicken to the skillet along with 1 tablespoon of Creole seasoning. Stir well to coat the chicken in the sauce and allow it to heat through for about 5-7 minutes.
Lower the heat and stir in ½ cup of sour cream until fully incorporated. Then, gently fold in the cooked angel hair pasta and mix until everything is well combined and heated through.
Sprinkle the shredded Jack cheese over the top of the pasta mixture. Cover the skillet with a lid for a few minutes to allow the cheese to melt into a gooey, delicious layer.
Serve the Chicken Enchilada Pasta warm, garnished with optional toppings like sliced black olives and chopped cilantro for an extra burst of flavor. Enjoy your culinary creation!