Preheat oven to 220C. Halve lobster lengthways with a sharp knife, remove tail meat and coarsely chop, refrigerate until required. Place shells on an oven tray and roast until orange in colour (15-20 minutes).
Transfer shells to a large saucepan, add onion, green onion, garlic, spices and 2½ litres water. Bring to the boil over high heat, reduce heat to low and simmer until stock is well flavoured (1¼-1½ hours).
Strain stock through a fine sieve into a saucepan (discard solids), bring to a simmer over medium-high heat, add peas and cook until just tender (1-2 minutes).
Divide lobster meat among bowls, ladle over broth with peas and serve immediately, scattered with tarragon.