Pound the chicken to 1/2 inch thick. Season lightly with salt and pepper (Cajun seasoning has salt too) on both sides. In a Ziploc bag, add the olive oil, Cajun seasoning, and the seasoned chicken. Seal bag and shake to distribute the seasonings evenly. Let it sit for 15 minutes.
Meanwhile, cook the fettuccine in salted water according to package instructions. Drain and set aside.
Heat some olive oil on a large skillet to medium heat. Cook the chicken, about 6-8 minutes each side, until cooked through or until internal temperature reaches 165 degrees F. Transfer to a plate and let it rest. Loosely cover with aluminum foil to keep warm.
Make the Alfredo sauce: wipe the skillet clean. On medium heat, melt butter and add garlic. Cook until fragrant, stirring, about 1-2 minutes. Add heavy cream and bring to a light simmer. Add the freshly grated parmesan cheese and the pinch of seasoning. Stir until melted, and season with salt and pepper to taste. Note: use freshly grated cheese as pre-bagged shredded cheese contains corn starch, which makes it hard to melt and does not lead to great results.
Add the cooked fettuccine to the sauce and toss to coat, until the pasta is warm.
Slice the chicken.
Serve the pasta with the sliced chicken on top. Garnish with diced tomatoes, chopped parsley, and more shredded parmesan cheese if desired.