Instructions

Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Mix the ground lamb, ground beef, mint, ginger, 1 teaspoon garlic, 1 teaspoon salt, and pepper in a large bowl until just combined. Divide evenly into four portions and shape in to large patties. Set aside. Mix Greek yogurt, lemon zest, 1 clove garlic, and 1/2 teaspoon salt in a bowl; cover and refrigerate.
Cook the lamb and beef patties on the preheated grill until the burgers are cooked to your desired degree of doneness, 3 to 4 minutes per side for well done. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C). Place the slices of onion and green tomato on the grill. Cook until lightly charred, about 1 minute on each side.
Spread yogurt sauce over the sliced ciabatta rolls. Assemble each burger by placing the patty on the the roll, and dividing the feta cheese slices over the patties. Top with a slice of grilled tomato, grilled onion, and 2 leaves of arugula, followed by the top half of the roll.