Season steak generously with kosher salt, pepper, and Cajun seasoning.
Heat avocado oil in a skillet over medium heat. Sear steak 3–4 minutes per side until desired doneness (see notes)*.
Turn heat to low, add 2 Tbsp butter, rosemary, and sliced garlic. Use a spoon to continuously baste the steak with the fragrant butter. Remove and rest steaks under foil.
Keep browned bits and remaining pan juices in the pan, but wipe out any burnt or blackened bits.
Turn heat to medium low. Melt 4 Tbsp butter and sauté minced garlic until fragrant.
Add cream, half and half, Cajun seasoning, salt, and pepper. Simmer 7–8 minutes until slightly thickened. While sauce simmers, cook pasta according to package instructions.
Stir in parmesan until melted and allow sauce to simmer until thickened. Slice the steak and pour any pan juices into the cream sauce. Finish by stirring in lemon juice to the sauce. Reserve ⅔ cup sauce.
Add pasta directly to sauce and toss to coat. Allow it to simmer in the sauce a few minutes if needed to help thicken the sauce.
Serve pasta topped with sliced steak, reserved sauce, parmesan, and parsley.