In a large pot, add the potatoes and enough water to cover. Bring to a boil, add salt and cook until tender, 15 minutes. Drain, return to the pot and mash with the cheese, cream and chives; season with salt and pepper.
Meanwhile, in a bowl, combine the beef, Worcestershire, garlic, grated onion, parsley, salt and pepper. Form 4 large patties. Drizzle with EVOO.
Preheat a cast-iron skillet over medium-high heat. Add the beef patties and cook, turning once, for 10 minutes for medium-rare.
While the burgers are cooking, heat a medium skillet over medium heat; add the butter. Add the sliced onion and cook until softened, 8 to 10 minutes. Add the mushrooms and cook until softened, 8 to 10 minutes more. Season with salt and pepper.
Divide the watercress and patties among 4 plates; top with the onion-mushroom mixture. Serve with the potatoes.