Heat grill to high. In a food processor, combine chickpeas, scallions, bread, peanuts, cumin, and ginger; season with salt and pepper. Pulse until roughly chopped. Remove half the mixture to a bowl; add egg to food processor. Process until smooth; add to reserved mixture in bowl, and mix well.
Form the mixture into four 3/4-inch-thick patties. Brush each side generously with oil; grill until charred, 3 to 5 minutes per side. Serve the burgers on English muffins with lettuce, mustard, and mayonnaise.