Season chicken on both sides with 1.5 Tbsp of Cajun spice. Heat pan to medium, add 2 Tbsp of oil and cook chicken until done. Turn chicken over in pan to avoid burning. Cook time should be roughly 12 minutes. Cut through chicken to make sure it is completely cooked, if not return to pan for a few more minutes. When the chicken is completely cooked cut it into strips and cover with foil to keep warm.
While chicken is cooking bring a stock pot of water to boil with 2 Tbsp of kosher salt added. When water comes to a boil add pasta and cook to within 1 minute of package instructions. I set a timer while cooking the pasta so I can tend to cutting the veggies and the chicken. Before draining pasta, reserve a mug of the pasta water.
Cut peppers and onions into 1/2" narrow strips. After chicken is removed, saute peppers and onions in pan on medium heat with 2 Tbsp oil. Cook time will be 5-10 minutes depending on how soft you want the peppers/onions to be.
When the peppers/onions are almost finished add chicken stock and cook for 2 minutes on high.
Lower heat to med-low, add tomatoes and green onions. Cook for 1-2 minutes, then add the cream to make the sauce. Add 1.5 Tbsp of Cajun spice and the chicken strips. Stir to incorporate and add the pasta-cook 1 more minute tossing it all together.
Test the dish to make sure it has enough flavor, if not add some more Cajun spice. It's really that simple. There is no extra salt in this dish, because most commercial Cajun spices' number one ingredient is salt.
Finally if the dish is too dry and you need a little more sauce add 1/2 cup of pasta water. I did not have to, but it is essential when making pasta to always save the cooking water for this reason.