Boil the linguine according to the package instructions until al dente, then drain and set aside.
In a large skillet, heat olive oil and 2 tablespoons of butter over medium-high heat. Season the steak with Cajun seasoning, smoked paprika, salt, and pepper, then sear for 2-3 minutes on each side until golden brown. Remove from skillet.
Melt the remaining butter in the same skillet over medium heat. Add minced garlic and sauté for about a minute until fragrant.
Add heavy cream and milk to the skillet, bringing to a gentle simmer. Stir in cream cheese, mozzarella, parmesan, and cheddar, mixing until melted and smooth.
Toss the cooked linguine in the cheese sauce, then fold in the seared steak. Serve immediately, garnished with chopped chives.
