Grilled Skirt Steak Quesadillas with Tomatillo Sauce

Preheat broiler to high. Remove and discard husks from tomatillos and cut each into quarters. Arrange tomatillos and jalapeños (skin-side up) on sheet tray and drizzle with 1 tablespoon olive oil; season with salt and pepper. Broil until softened and golden, 7 minutes. Let cool slightly, then thinly slice jalapeños into thin strips. In blender, combine tomatillos, 1/3 sliced jalapeños, lime juice, garlic, cilantro, onion, and 2 tablespoons olive oil until smooth. Season with salt and pepper. Heat grill pan over high heat. Season steak with salt and pepper and rub with 1 tablespoon olive oil. Grill 3 minutes per side for medium-rare, then transfer to a cutting board to let rest, 5 minutes. Thinly slice on the diagonal. In small bowl, combine butter and remaining 1 tablespoon olive oil. Preheat large nonstick skillet over medium-high heat. Layer 1 tortilla with steak, 1/2 cup of cheese, and jalapeño. Top with second tortilla and brush top and bottom with butter-olive oil mixture. Cook quesadilla in skillet 2 to 3 minutes per side, or until tortillas are golden and cheese is melted. Repeat with remaining ingredients. Cut into quarters and serve with tomatillo sauce, sour cream, and lime wedges. Garnish with cilantro leaves.