Peel the potatoes, then slice into thin wedges or cut into 3/4-inch dice. Heat a skillet over medium-high heat and add a drizzle of EVOO. Add the bacon and cook until crisp, then drain on a paper-towel-lined plate. Add the potatoes to the fat in the skillet and season with a little salt and lots of pepper. Cook until browned, 5 to 6 minutes. Cover with foil and cook for 5 minutes. Remove the foil and cook until crisp, 7 to 8 more minutes.
Mix the sour cream, chives, dill, garlic, horseradish, 2 tablespoons parsley and half-and-half or milk in a small bowl. Season with salt and pepper.
Mix the beef, Worcestershire sauce, dry mustard cayenne or hot sauce and the remaining 2 tablespoons parsley in a large bowl. Sprinkle with salt and lots of pepper.
Heat a cast-iron skillet or griddle over medium-high heat. Brush with oil, then add the beef mixture in 4 loose balls of equal size (do not shape them with your hands). Flatten with a spatula into 3/4-inch-thick patties. Scatter the onion slices over the top and press in with the spatula. Cook for 3 minutes, then flip and press the onion into the patties. Cook for 2 more minutes. Douse the pan with the beer and lay the cheese over the patties. Cover and cook until the cheese melts, about 1 minute.
Serve the burgers on the rolls with pickles and watercress. Drizzle the horseradish sauce over the potatoes and serve on the side.