Cook pasta to al dente according to package directions. Drain and set aside on until ready to use.
Meanwhile,in a large, deep skillet, melt 1 tablespoon olive oil and 1 tablespoon butter. Add chicken pieces to the skillet and season with the cajun seasoning and 1/2 teaspoon kosher salt. Cook for 4-5 minutes, until chicken is fully cooked through. Transfer to a plate and set aside.
To the same skillet, add 3 tablespoons of butter and the minced garlic. Cook for about 30 seconds to a minute.
Whisk in 1/4 cup of chicken broth and stir constantly to deglaze the pan (loosen and scrape up all the brown bits of flavor from the bottom of the pan), then stir in flour and cook for 1-2 minutes.
Whisk in milk and remaining chicken broth and simmer for several minutes until thickened (sauce should coat the back of a spoon).
Remove from heat and gradually add in the Parmesan cheese a little at a time until it's fully melted and incorporated.
Toss the cooked pasta and chicken with the sauce to coat.
Serve immediately, garnished with diced tomatoes and fresh chopped parsley, if desired.
Notes
Adjust the heat level to your liking by adding more of less of the cajun seasoning.