Plunge your lobster in a large pot of boiling water until red and cooked, about 8 to 10 minutes. Remove from the boiling water and let cool enough to be handled.

Crack the claws and knuckles, remove the meat and set aside. Remove the tail meat in a single piece and set aside.

Whisk the eggs with the coconut milk and dill in a bowl. Season to taste with sea salt and freshly ground black pepper;

Heat a non-stick skillet over a medium heat, add 1 tablespoon cooking fat and pour the egg mixture into the skillet.

Use a spatula to stir the omelet gently while it cooks and to allow uncooked parts to run underneath.

When almost set on top, add the lobster’s claw and knuckle meat and fold the omelet in half and cook, covered, for another minute.

Serve the omelet topped with slices of the lobster’s tail meat.