Heat grill to medium-high.
Pulse parsley, capers, oregano, and garlic in a food processor until finely chopped. Add vinegar, red pepper, 1/4 cup oil, and 1/4 teaspoon each salt and pepper; pulse until well-blended. Rub 3 tablespoons salsa all over steaks; reserve remaining sauce for serving.
Heat butter and remaining 1/4 cup oil in a large skillet over medium heat. When butter melts, add the potatoes, shallots, bay leaves, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Stir to evenly coat. Immediately reduce heat to low, cover, and cook, stirring occasionally, until a knife pierces through the potatoes easily, 15 to 20 minutes.
While potatoes cook, generously season steaks with salt and pepper. Grill, turning once, for 6 to 8 minutes for medium-rare. Let rest for 5 minutes before slicing. Serve with potatoes, shallots, and reserved salsa.
Wine Pairing: Merlot