Creamy herb sauce: Stir together cilantro, scallion, mint, lemon juice, lemon zest, Greek yogurt, and a pinch of salt until combined.
Onion saute: Heat oil, then add red onions to a large saute pan over medium-high heat.
Cook until they begin to soften but still retain their color and crunch, about 2 minutes. Set aside.
Burgers: Combine the lamb, cumin, sichuan peppercorns, chile flakes, sesame oil, sugar, mustard, and salt in a large bowl. Mix gently until spices are evenly distributed, but don’t overwork meat. Form into four balls.
In the same large saute pan used for the onions and peppers, heat a tablespoon of oil over medium-high heat. Use a wide, stiff spatula to gently smash the balls into flat patties, about 3⁄4-inch (2-cm) thick.
Cook until the bottom of each burger has formed a brown crust, about 3–4 minutes. Flip each patty and cook through, approximately 3–4 minutes.
Assembly: Spread about 1 tablespoon creamy herb sauce on the bottom of each bun. Place a burger on each bun, topping each with a spoon of onions, sliced cucumber, chilis, and cilantro.