Combine meat with parsley, Worcestershire, garlic, onion grated over the bowl to catch the juices and lots of salt and pepper. Form 8 3-ounce patties, making them a little thinner at center for even cooking. Arrange them on a plate and drizzle with EVOO to coat.
Heat a cast-iron skillet or griddle pan over medium-high heat.
Heat a liberal drizzle of EVOO in a non-stick skillet over medium-high heat, just enough to coat the bottom. Add potatoes in a single layer and season with salt and pepper. Turn occasionally and cook until brown and crispy, 10-12 minutes.
In food processor, combine milk, cheese and sour cream. Process until a smooth, thick sauce forms. Add an extra splash of milk as necessary.