Mix the mayonnaise and grated garlic together in a small bowl and season with salt and pepper. Set aside.
Heat 1 tablespoon of the oil in a medium skillet over medium heat. Add the onion and cook, stirring, until soft, about 5 minutes. Add the chopped garlic and cook, stirring, until fragrant, about 2 minutes. Let cool slightly.
Gently mix the ground beef, almonds, olives, raisins, tomato sauce, allspice, cinnamon and 1 teaspoon salt in a large bowl until just incorporated. Divide the meat mixture into 16 equal portions and form into patties.
Wipe out the skillet, add the remaining 2 tablespoons oil, and heat over medium-high. Working in batches, cook the patties, flipping once until browned on each side and medium on the inside, about 2 minutes per side. Serve on the potato rolls with a smear of the garlic mayonnaise and a lettuce leaf.
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