Mash the anchovy fillet into a paste on a cutting board with the side of a chef’s knife. Sprinkle the garlic with a pinch of kosher salt and mash it into a paste.
Put the butter in a small microwave-safe bowl and microwave it on high in 10-second bursts until it just begins to melt. Mash the butter with a fork and stir in the anchovy, garlic, parsley, capers, lemon zest, and a few grinds of black pepper.
Heat the oil in a 10-inch skillet (preferably cast iron or French Steel) over high heat. Season the steaks generously with salt and pepper. Sear the steaks on all sides until a meat thermometer reads 130°F- 135 for rare or 140 - 145°F for medium rare. 155 - 160 for medium. Serve each steak topped with a dollop of the butter.
When pan searing steak, get the pan nice and hot. Don't turn the steaks until they release easily with tongs.