Add Cajun seasoning and 1 tablespoon of olive oil to large plastic zipper bag and mix together. Add chicken and toss to coat. Add remaining olive oil to medium skillet and heat to medium high. Cook chicken until cooked through, about 6 minutes each side. Place on a plate and cover with foil.

Bring a pot of water to boil. Add about 2 tablespoons of salt to water and then add pasta. Cook until al dente. Scoop out of water with a slotted spoon and into a large bowl. Cover pasta to keep warm. Keep pasta water in case we need it for the sauce.

In a large skillet, melt the butter. Add garlic and cook until fragrant, about 1-2 minutes. Add lemon zest and then gradually whisk in heavy cream. Let cream cook until it begins to bubble. Add Parmesan cheese and stir to combine. Let sauce thicken for another couple of minutes. If it gets too thick, add a little pasta water to thin it out. Give the sauce a taste. Add salt and pepper, as needed. Add tomatoes and toss to get them warmed up.

Add pasta to skillet with the sauce. Slice chicken into bite-sized pieces and add to pasta. Add chopped parsley and toss everything together. Top with a few more tomatoes, parsley, and cheese for garnish. Serve immediately.