Bring steaks to room temperature, and season with salt and pepper before grilling or griddling. Heat cast-iron griddle or skillet over medium-high heat, add olive or canola oil, 2 turns of the pan, and cook steaks 8-10 minutes for medium-rare to medium doneness, adding halved lemon to skillet for last 2 minutes to caramelize. Remove steaks from pan, and let rest 5-10 minutes before slicing against the grain, then douse with juice of ½ lemon.
For salsa verde, place parsley, mint, anchovies, capers, garlic, shallot, juice of ½ lemon, red wine vinegar, Worcestershire, red chili flakes and EVOO in food processor, then pulse process into sauce and add salt and pepper to taste.
For the fried green tomatoes, arrange the sliced green tomatoes on kitchen towels or paper towels. Season with salt and let them drain 20 minutes.
Arrange breading station: flour, eggs and breadcrumbs combined with panko, cheese and remaining spices and sesame seeds. Season flour, eggs and breadcrumbs with salt and pepper. Dredge each tomato through the flour, egg and breadcrumb mixture. Heat ⅛-inch frying oil over medium-high heat, cook tomatoes 2-3 minutes on each side to deep golden brown and drain on wire rack.
Arrange sliced steak on large plates and top with salsa verde. Fan 3 fried green tomatoes alongside the steak and serve with lemon wedges and dot with finely chopped hot pickled cherry peppers.