Cook pasta according to package directions on the box. Drain and set aside.
Pat dry the chicken breasts with a paper towel. Season with cajun seasoning and rub it all around.
Heat olive oil in a large skillet or cast-iron pan over medium-high heat. Add chicken and cook for 5-6 minutes, flip, and cook for an additional 6-7 minutes. (If using large chicken breasts, cut them in half horizontally to make thinner cuts. They will cook quicker.) Remove chicken to a plate and cover with foil.
Melt butter in the same skillet or saucepan. Add diced onion and saute for 3-4 minutes. Add in the minced garlic, and cook until fragrant, about 1-2 minutes.
Whisk in heavy cream, lemon zest, and grated parmesan. Whisk for 2 minutes or until the sauce has thickened. Season with salt and pepper, to taste.
Slice the chicken and add on top of the pasta. Spoon the sauce over the top and then garnish with diced tomatoes, parsley, green onions, and shredded parmesan. Enjoy immediately.