Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. (You could also preheat a grill pan or a large nonstick skillet over medium high heat or, preheat outdoor grill instead of the skillet).
While the pan is heating up, combine the meat with about 3 tablespoons of grated red onion, Worcestershire, grill and poultry seasonings or salt and pepper. Form two-inch meatballs, then flatten them into patties.
Cook the mini burgers for 3 minutes on each side then top with cheese. Tent the mini cheeseburgers loosely with foil to help the cheese melt.
While the burgers are cooking, whisk together the mustard and cider vinegar in a large salad bowl. Continue whisking and stream in the remaining 2 tablespoons EVOO and season with salt and pepper.
Finely chop up the remaining red onion and add it to the bowl along with the romaine, pickles and tomatoes. Toss the salad to evenly coat everything in dressing.
To serve, arrange the salad on a large platter and slide the burgers on top.