Halve lobster lengthways with a sharp knife. Bring a large saucepan of water, fitted with a bamboo steamer, to the boil over high heat.
Remove green tops from green onion and thinly slice diagonally. Place in a bowl of cold water, set aside. Finely chop remaining green onion, combine in a bowl with soy sauce, Shaoxing wine, ginger and 1 tbsp water, and whisk to combine.
Place lobsters cut-side up on plate that fits inside steamer, spoon over three-quarters of sauce and steam, covered, until just cooked through (12-15 minutes). Scatter with onion tops and serve with rice and remaining ginger sauce to the side.