Kill the lobster humanely, halve lengthways and clean well.
Pound the coriander roots, garlic and shallots in a mortar with a pestle to form a fine paste. Heat
Heat a grill or barbecue to hot. Brush the lobsters with the remaining oil and place them, cut-side-down, on the grill. Cook for 3–4 minutes, then turn and cook until just cooked through. Leave to rest for 5 minutes in a warm place.
Chop each lobster half into three pieces and arrange on a plate. Drizzle the sauce over the top to serve.