Heat the oven to 400°F. Lightly grease a 9x13-inch baking dish and set aside. Bring a large pot of well-salted water to a boil.
Season the chicken: Pat chicken dry and place in a bowl. Add Cajun seasoning (for chicken), onion powder, lemon zest, kosher salt, black pepper, and 1 tablespoon olive oil. Toss to coat and let sit for 10 minutes while the water comes to a boil.
Cook the pasta: Drop fettuccine into the boiling water and cook until 2 minutes shy of al dente. Reserve 1/2 cup pasta water if desired, then drain and set aside.
Sear the chicken: In a large oven-safe skillet over medium-high heat, add 1 tablespoon olive oil. Sear chicken until browned and cooked through, 4 to 5 minutes per side (165°F internal). Transfer to a cutting board, tent with foil, and rest 5 minutes before slicing into strips or bite-size pieces.
Build the sauce: Reduce heat to medium and add butter to the same skillet. Stir in garlic and cook 45 to 60 seconds until fragrant. Add tomato paste and the Cajun seasoning (for sauce), cooking 1 minute to darken and bloom the spices.
Deglaze and simmer: Pour in chicken broth, scraping up any browned bits. Stir in heavy cream and bring to a gentle simmer. Cook 3 to 4 minutes, stirring, until slightly thickened.
Finish the sauce off the heat: Remove skillet from heat and gradually whisk in the grated Parmesan until smooth. Stir in lemon juice and chopped parsley. Taste and season with additional salt and pepper if needed. If very thick, loosen with a splash of reserved pasta water.
Combine and assemble: Add the drained pasta and sliced chicken (along with any resting juices) to the skillet and gently toss to coat. If your skillet isn’t oven-safe or is very full, transfer everything to the prepared baking dish. Sprinkle the top with the extra 2 tablespoons Parmesan.
Bake 8 to 10 minutes until bubbling around the edges. For golden spots, switch to broil for 1 to 2 minutes, watching closely. Rest 5 minutes, then garnish with parsley and serve hot.