Add all ingredients for dressing to the bowl of a small food processor and pulse to combine. Remove to bowl and set aside to allow the flavors to blend.
Mix all the ingredients for burger patties (do not overwork). Divide the meat into 4 equal patties that are a little larger in diameter than the size of your bun, so that when they shrink after cooking they will fit the buns perfectly.
Heat a grill pan, cast iron skillet, or outdoor grill to medium heat. Once the grill is hot, cook burgers about 3 to 4 minutes per side, or until desired doneness is reached. Do not overcook or the burgers will be dry.
Top each burger with mozzarella cheese during the last 2 to 3 minutes of cooking.
Lightly toast the cut sides of your buns either on the grill or under the oven broiler.
Spread some of the feta dressing on the bottom half of each bun, top with a burger patty, romaine lettuce, sliced tomato, red onion, banana pepper rings, and sliced cucumber. Spread some feta dressing on the top halves of the buns and cover the burgers.
Grab lots of napkins! If you've done it right you'll need them! Enjoy - and maybe even go back for seconds! (Yes - it's that good!)
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.