MAKE THE COMPOUND BUTTER. In a small bowl, stir the butter, tomato paste, parsley, capers, and anchovy paste with a small rubber spatula until well combined.
Place the butter onto a piece of parchment paper and form into a log, using the paper to manipulate the butter.
Twist the ends of the paper to seal.
Wrap the parchment roll in plastic wrap and refrigerate for at least 30 minutes; slice with a warm knife, to serve.
MAKE THE STEAKS. Remove the steaks from the refrigerator 30 minutes before cooking.
Pat both sides of the steaks with paper towels to remove any moisture.
Generously season both sides of the steaks with salt and pepper.
Meanwhile, preheat a large cast-iron grill pan over high heat.
Lightly brush both sides of the steak with the olive oil.
Place 2 of the steaks onto the grill pan.
Cook for 1 ½ minutes, then rotate the steak 90 degrees and cook an additional 1 ½ minutes, to create a crosshatch.
Flip the steak. Cook for 1 ½ - 2 minutes more.
Transfer the steaks to a cutting board, cover with foil and rest for 5 minutes.
Let the pan reheat for a few minutes; repeat with the remaining steaks.
To serve, top with a generous slice (or two!) of Puttanesca Butter.