Fill a large pot with water and bring it to a boil for the angel hair pasta. You want to make sure the water is bubbling vigorously before adding the pasta. Once it’s boiling, add a pinch of salt to season the pasta.
In another large pot, heat some olive oil and butter over medium-high heat. Watch as the butter melts and begins to bubble; this is the perfect time to add the next ingredients.
Add the chopped onion and green chilies into the pot. Sauté them for about seven minutes, stirring occasionally, until the onions become translucent. You want them soft but not browned for the best flavor.
Now it’s time to add the all purpose flour. Stir it into the mixture and let it cook for about a minute. This process helps eliminate the raw flour taste and begins the thickening process.
Pour in the chicken broth and bring the mixture to a boil. The sauce should start to thicken up nicely at this point. Make sure to keep stirring to prevent any lumps from forming.
Add the chicken breasts, seasoned with creole seasoning. Let it simmer over medium heat for about 15 to 20 minutes. You want the chicken to be fully cooked and tender, so keep an eye on it.
While the chicken is cooking, go back to your boiling pot and add the angel hair pasta. Cook it until al dente, which usually takes around three to four minutes. Once done, drain the pasta and set it aside.
Once the chicken is cooked through, remove it from the pot and shred it using two forks. Then return the shredded chicken to the saucy mixture.
Add the sour cream and one cup of shredded Jack cheese to the chicken mixture. Stir until everything is well combined and let it simmer for another five minutes. The sauce should be creamy and rich at this stage.
Finally, add the drained angel hair pasta to the pot and stir gently to coat the pasta evenly with the sauce. Serve it hot, garnished with additional shredded cheese, cilantro, and sliced black olives if desired.
