Mix sour cream with vinegar, sugar, salt and pepper. Stir in ketchup and relish, and reserve.
For the onions, heat EVOO, a couple of turns of the pan, in a skillet over medium heat. Add onions and season with salt and pepper. Cook to light brown, 15 minutes, add stock and cook 10-15 minutes more until very soft and tender.
Combine beef with garlic, Worcestershire, parsley, Kosher salt (specifically Kosher salt gives meat a good crust) and pepper. Form 8 4-ounce, thin patties. Drizzle with EVOO to coat lightly then sprinkle with a little extra salt. Top each patty with 1 tablespoon Dijon mustard or grainy Dijon.