Preheat a cast-iron griddle or skillet.
In a small bowl, combine ketchup, sour cream, relish, salt, pepper and tarragon. Reserve.
Combine ground meat with artichokes, spinach, cheese, garlic, thyme and lemon zest. Form 6 patties and drizzle each with olive oil.
Toast buns.
Spread soft cheese or goat cheese on bun bottoms, top with a patty, spinach, tomato and onion. Slather bun tops with tarragon sauce, set tops in place and serve with crispy, thin oven fries tossed with garlic and cheese alongside.