In a small skillet, toast the peppercorns over medium heat until fragrant, about 30 seconds; let cool. Transfer the peppercorns to a mortar or spice grinder and grind to a powder. Set aside.
Heat oil in a large cast iron skillet or wok over high heat. Add garlic and cook, stirring, until fragrant, about 30 seconds. Add lamb, jalapeno, cumin, sichuan peppercorns and season with salt and pepper. Cook, breaking up with spoon and pressing firmly to help brown, until fully cooked and crispy, about 8-10 minutes.
Meanwhile, blanch beans by boiling for 45 seconds, then draining and setting aside.
In a small bowl combine soy sauce, lime juice, and brown sugar. Stir until sugar dissolves.
Combine cooked lamb with blanched green beans, soy mixture, cilantro, and green onions and toss to combine.
Serve over rice. Garnish with additional lime wedges on the side.