Place the garlic and salt on a small plate and, using the back of a fork, mash into a paste.
In a large bowl, combine the lamb, mint, parsley, cumin, coriander, cinnamon, allspice, and cayenne and season with salt and pepper to taste. Form the mixture into 8 meatballs. Let sit for 30 minutes to come to room temperature, and for the flavors to combine.
Heat a grill pan over high heat and brush with oil. Flatten the lamb meatballs slightly to to create 1-inch thick patties. Grill for 3 minutes until a nice crust forms; flip and grill for an additional 2-3 minutes for medium.
Serve on mini toasted pitas with a dollop of tzatziki sauce and a few arugula leaves. (Also delicious: roasted grape tomatoes and/or thinly sliced red onion.)
*Ozery Bakery makes some multi-grain slider buns called “Just Minis” that are the perfect size for this recipe. They’re also really good!
Roughly grate the cucumber on a box grater (or, alternately, finely chop by hand). Place in a paper towel-lined seive and squeeze out an additional moisture.
Mash the garlic, salt, and lemon juice together on a small plate (this makes the garlic have less of a bite). Pour into a medium-size bowl and whisk in the yogurt, olive oil, and mint. Season with salt and pepper to taste. Let sit for an hour (or more) in the refrigerator for the flavors to combine.
Serve with the lamb sliders.