Pat steaks completely dry with paper towels. Season generously on both sides with 1 teaspoon salt and all the pepper. Let sit at room temperature for 30 minutes while you prep the shrimp.

Toss shrimp with remaining 1/2 teaspoon salt and paprika. Set aside.

Heat oil in a large cast iron skillet over medium-high heat until shimmering. Add steaks and sear undisturbed for 4 minutes until a deep brown crust forms. Flip and cook 3-4 minutes more for medium-rare, or until internal temperature reaches 130°F. Transfer to a plate and tent loosely with foil.

Reduce heat to medium. Add 2 tablespoons butter, garlic, and thyme to the pan. Once butter foams, tilt pan and spoon over steaks for 1 minute if still in pan, or reserve to drizzle over at serving. Remove from heat.

Return pan to medium-high heat. Add shrimp in a single layer and cook 2 minutes without moving. Flip and cook 1-2 minutes more until pink and opaque throughout. Add remaining 1 tablespoon butter and lemon juice, tossing to coat.

Slice steaks against the grain and arrange on plates with shrimp alongside. Spoon any pan juices over top and sprinkle with fresh parsley. Serve immediately.