Preheat a grill to medium high. Bring a medium saucepan of water to a boil; add the scallions and cook until wilted, about 45 seconds. Remove with tongs to a colander to cool, then pat dry. Add the broccoli to the boiling water and cook until just beginning to soften, about 3 minutes. Drain and transfer to a large bowl.
Heat 1/2 tablespoon vegetable oil in a small nonstick skillet over medium heat. Add the peanuts and half each of the ginger and garlic; cook, stirring, until toasted, 2 to 3 minutes.
Pound the beef until 1/8 inch thick. Lay 2 pieces next to each other, overlapping slightly; season with salt and pepper. Top with a quarter of the scallions, laying them crosswise. Roll up the meat around the scallions; secure with toothpicks. Repeat to make 3 more rolls.
Add the asparagus, any remaining scallions and the remaining 2 tablespoons vegetable oil to the broccoli; season with salt and pepper and toss. Mix the hoisin sauce, soy sauce and remaining ginger and garlic in a bowl.
Oil the grill grates. Brush the steak rolls with half the sauce. Cover and grill, turning and brushing with the remaining sauce halfway through, until charred, 7 to 8 minutes. Grill the vegetables until tender, 3 to 5 minutes. Halve the steak rolls, remove the toothpicks and serve with the vegetables. Top with the peanut mixture.