In a zip-top bag, combine lemon juice, white wine vinegar, shallots, garlic, olive oil, dried oregano, dried rosemary, black pepper and kosher salt. Add flank steak, seal bag and marinate in the fridge for 2 to 3 hr.
Remove steak from marinade (discard marinade) and grill over direct high heat for 5 to 6 minutes on each side for medium rare. Let steak rest about 10 min before slicing.
In a blender or small food processor, blend anchovy fillet, garlic, kosher salt, lemon zest, lemon juice and red wine vinegar. Scrape down sides of blender and add packed parsley leaves, chopped thyme and olive oil; blend until just smooth and drizzle over flank steak.
• For the most tender steak, cook to no more than medium (better: medium rare) and cut across the grain into thin slices.