Ingredients

2 Kirby cucumbers, divided
1 1/2 cups Greek yogurt (3/4 pounds)
1 teaspoon fresh lemon juice, divided
5 garlic cloves, minced, divided
1 pint grape tomatoes, quartered
1 small red onion, halved and thinly sliced
1/3 cup chopped flat-leaf parsley
1/4 cup chopped mint
 1/4 cup extra-virgin olive oil
 1 rounded teaspoon dried oregano
1 rounded teaspoon dried rosemary, crumbled
1 (12-ounces) package naan bread (four 8-inch pieces)
or 4 (8-inch) pocketless pita rounds
1/2 roast chicken, skin discarded, meat shredded (about 2 1/4 cups), and carcass reserved for stock
 1/2 head iceberg lettuce, thinly sliced

 
Preparation

Preheat broiler.
Peel and grate 1 cucumber, then squeeze it with your hands to remove excess water. Stir together with yogurt, 1/2 teaspoon lemon juice, one third of garlic, and 1/4 teaspoon each of salt and pepper to make tsatsiki.
Cut remaining cucumber into 1/4-inch pieces and stir together with tomatoes, onion, parsley, mint, remaining 1/2 teaspoon lemon juice, and 1/4 teaspoon each of salt and pepper to make salsa.
Gently simmer oil, oregano, rosemary, remaining garlic, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a small heavy saucepan, stirring constantly, until garlic is fragrant but not browned, 1 to 2 minutes. Toss chicken with 3 tablespoons garlic oil and brush one side of bread with remainder.
Heat bread, oiled side up, in a 4-sided sheet pan, covered with foil, 3 to 4 inches from broiler 3 minutes. Uncover and broil, rotating bread for even coloring, until golden in spots, about 2 minutes.
Spread some of tsatsiki on warm bread and top with chicken and some of lettuce and salsa. Serve remaining lettuce, salsa, and tsatsiki on the side.