Place the water, wine, leek, carrot, lemon, bay leaves, peppercorns, fennel seeds, and salt in a large pot. Bring to a low simmer over medium-low heat, stirring occasionally.

Simmer for 10 minutes, to extract as much flavor from the ingredients as possible, before adding your lobster tails. Adjust the temperature to keep the court bouillon from boiling and slowly poach the lobster tails for 15-20 minutes or until cooked through.

Remove the tails from the pot and submerge in a bowl filled with ice water. Set aside to cool completely before serving.