In saucepan, heat butter over medium heat until it starts to brown and smells nutty, 3 to 4 minutes. Add anchovies and break with wooden spoon until they almost fall apart. Add chopped parsley and cook for 1 more minute. Set aside.
Heat oven to 375°F. Season steak on both sides with salt. Heat cast-iron skillet or heavy oven-safe frying pan over medium-high heat, add oil and butter and heat until foamy and smoking. Add steak and garlic and don’t move steak for 2 to 4 minutes. Lift corner of steak to check for a deep-brown crust before turning over. Flip and cook for a maximum of 4 minutes for a 2-to-2 1⁄2-inch-thick steak.
Cook in oven until medium-rare. Remove and place steak on serving platter; cover loosely with aluminum foil. Let rest for 5 minutes.
Heat anchovy butter over low heat.
Reheat oil over medium heat to 375°F and cook fries a second time until crispy, 4 to 5 minutes. Transfer to paper-towel-lined tray; season with salt while hot.
Cut steak into thick slices; season with pepper and top with anchovy-parsley butter.