Preheat a grill to indirect heat, low setting, approximately 325 degrees F.
In a medium bowl, add the lamb, garlic, red onion and feta. Sprinkle with salt and pepper. Mix well with your hands. Form the mixture into 16 small patties (about 2 1/2 inches in diameter and 1 1/4-inch thick). Use your index finger to press a shallow dimple into the center of each patty. Cover and place in the refrigerator until ready to grill.
In a small bowl, combine the balsamic vinegar, pomegranate molasses and soy sauce.
Oil a paper towel with the canola oil and wipe down the grill grates several times to well coat with the oil. Immediately place the patties on the grill (dimple-side down) and cook for 8 minutes. Turn over, baste the tops with the balsamic mixture and cook for 4 to 6 minutes more (or to 130 degrees F for medium rare and 140 degrees F for medium).
Remove from the grill and place on the Hawaiian sweet rolls or potato rolls. Add 2 slices of cucumber and a teaspoon of the Mint Aioli. Serve garnished with mint leaves.
Mince the garlic, and then sprinkle the salt on top, and continue to mince and smash the salt into the garlic to form a paste. In a small bowl of a food processor fitted with the steel blade, blend the yolks, garlic paste, lemon juice and mustard powder. Slowly add the olive oil to the yolk mixture in a very slow steady stream until the mixture is emulsified. Add the fresh mint and pepper and pulse until incorporated. Refrigerate.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.