How to Make It
In a small bowl, combine the parsley, rosemary, thyme, garlic and olive oil. Spread the mixture all over the steak. Cover and refrigerate on a platter for at least 4 hours or overnight.
In a food processor, combine the parsley with the basil, mint, capers, anchovies, garlic, mustard and sugar and process to a paste. With the machine on, slowly pour in the olive oil. Season with salt and black pepper.
Light a grill. Scrape most of the marinade off the steak and season the meat with salt and black pepper. Grill over high heat for about 3 minutes. Turn the steak and grill for 2 minutes longer, until browned outside and medium-rare within. Transfer the steak to a cutting board and let rest for 3 minutes. Thinly slice the steak against the grain and sprinkle with smoked paprika. Pass the salsa verde at the table.