1 small red onion, 1/2 minced and 1/2 thinly sliced
2 1/2 pounds ground lamb
6 medium scallions, minced
1/2 cup minced mint leaves
1/2 cup freshly grated Parmigiano-Reggiano cheese
1 1/2 teaspoons finely grated lemon zest
Freshly ground pepper
1/4 teaspoon cayenne pepper
1 medium tomato, thinly sliced
1 small cucumber—peeled, halved, seeded and thinly sliced
3/4 cup plain yogurt
6 hard rolls, split and lightly toasted
In a food processor, combine 3 tablespoons of the lemon juice with half of the minced jalapeños, the cilantro leaves, ginger, sugar, minced onion and 1/2 teaspoon of salt. Process until pureed. Transfer to a bowl and refrigerate.
Light a grill. In a large bowl, combine the ground lamb with the remaining minced jalapeños, the scallions, mint, cheese, lemon zest and 2 teaspoons of the lemon juice. Add 1 teaspoon of salt, 1/2 teaspoon of pepper and the cayenne and mix gently with your hands. Pat the meat into 6 burgers.
In a medium bowl, toss the tomato, cucumber and sliced onion with the remaining 1 tablespoon plus 1 teaspoon of lemon juice. Season with salt and pepper.
Grill the burgers over a hot fire until nicely charred on the outside and pink within, about 4 minutes per side. Fold the yogurt into the cilantro puree. Spread some of the yogurt sauce on the bottom half of each roll; top each with a burger, another dollop of yogurt sauce and some of the tomato-cucumber salad. Close the sandwiches and serve.