Make the salsa verde: Pulse the parsley, scallions, capers, lemon zest and juice, anchovies, garlic, mustard and olive oil in a food processor until slightly chunky. Pour into a bowl and season with salt.
Preheat a grill to high or place a grill pan over high heat. Pierce the steak all over with a fork and season with salt and pepper. Oil the grill or pan; grill the steak, 4 to 5 minutes per side for medium-rare, turning once. Transfer to a cutting board and let rest for 5 minutes.
Slice the tomatoes and season with salt and pepper. Thinly slice the steak against the grain. Serve with the tomatoes and salsa verde.