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Cajun Seasoning: Mix it all together and keep it in the glass jar or container with a lid. It should be used within 6 months.
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Boil water for the spaghetti and add about 1 tablespoon of salt. When it boils add pasta and cook according to the package. Do not overcook it. Drain and set aside.
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Cut chicken breast into bite-size pieces and season it with Cajun Seasoning. About 2 teaspoons for everything, but you may add later some more. Heat the pan or a skillet with oil and cook chicken on a medium high temperature. Turn after 2-3 minutes and keep turning until it cooks through. Internal temp for the chicken breast is 165F. Place it on the kitchen paper towel until ready to serve. Or you can do cook chicken at the same times as pasta/sauce so it all finish at the same time.
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On the other side, heat the skillet or a pan with olive oil and butter. Add sliced peppers and onion. Cook it for approximately 10-12 minutes on a medium-high heat, stirring often to prevent from burning. You want peppers to be cooked but not over-cooked, so you are looking that they are still holding a form and have a bit of crunch.
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While the peppers are cooking mix roux by combining whole milk with a tablespoon of flour. Mix until there are no more lumps. Yes, you can technically use whipped cream but milk works fine when you mix it with a bit of flour.
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Add ROUX to the peppers and stir. It will start to come together as soon as you see that the milk is heating through. If it's too thick, then just add a splash of milk and stir, otherwise, continue with the next step which is adding shaved parm cheese and 1/2 teaspoon Cajun seasoning to give your sauce extra edge. Stir again. It will start to thicken. You may try the sauce to see if you need a bit more salt or other seasonings.
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Add cooked pasta and mix to coat, then add a bit of dried parsley and more shaved parm cheese if you wish.
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Serve it with the cajun chicken immediately.