Combine the water, salt, sugar, and the juiced lemon in a large pot and bring to a rolling boil.
Turn off the heat completely.
Immediately add the shrimp and poach for 3 minutes.
Remove the shrimp with a spider or slotted spoon and transfer to a paper towel-lined tray. Refrigerate for 20 minutes, or until completely cool.
Cut the shrimp into bite-sized pieces and pat dry.
In a bowl, gently fold together the shrimp, mayonnaise, chives, salt, lemon zest, and lemon juice. Taste and adjust with additional salt or lemon juice if desired.
Heat the oil in a nonstick skillet over medium heat and toast the inside of the brioche buns until golden brown.
Spread a thin layer of mayonnaise inside each bun, fill generously with the shrimp mixture, and garnish with extra chives and freshly ground black pepper.