Place bulgur in a microwave-safe bowl. Add enough water to cover. Microwave on high until bulgar absorbs water, 1 to 2 minutes. Stir, then set aside to cool.

Place mint leaves in the bowl of a food processor. Process, gradually adding onion through the feed tube until mixture is finely chopped. Stir mint-onion mixture into bulgur. Stir in cumin, allspice, salt, and pepper.

Stir bulgur mixture into ground lamb until well combined. Using damp hands, shape lamb mixture into small, palm-sized patties.

Add oil to a large skillet over medium heat. Cook kibbeh patties until golden brown and cooked through, turning once, about 6 minutes on each side.