Bring a large saucepan of water to the boil and reduce to a simmer over medium heat. Poach the lobster tails in their shells for 15–20 minutes until cooked – a probe thermometer is useful here, with the ideal internal temperature being 63°C. Remove the lobster tails from the pan and set aside to cool, then refrigerate until chilled.
Preheat the oven to 180°C fan-forced (200°C conventional).
Remove the lobster meat from the shells and slice into eight discs per tail. Finely chop any small or discoloured pieces of lobster you may have leftover.
Combine the mayonnaise, lemon juice, vinegar and mustard powder into a small bowl. Slowly add the oil while whisking continually. Season to taste.
Butter the brioche buns lightly. Place them, buttered side down, in an ovenproof frying pan and toast in the oven for about 5 minutes until golden brown.
Spread 1 teaspoon of the mayonnaise on each buttered half of the brioche buns. Place 1 tablespoon of the chopped lobster on the bottom bun and season to taste. Arrange two slices of lobster meat on top without overlapping. Add ½ teaspoon of mayonnaise to each lobster slice and season again to taste. Add a few slices of shallot and a few pieces of watercress, close with the top buns and serve immediately.
