Heat the oil in a saucepan over medium heat. Add the shallot, garlic, and ginger, and cook for 2 to 3 minutes, until fragrant and softened.
Add the curry paste and cook for 1 minute, stirring constantly, until it darkens slightly and smells noticeably deeper.
Whisk in the coconut milk. Bring the sauce to a bare simmer and hold it there for 10 to 12 minutes, until it thickens slightly.
Stir in the fish sauce, lime juice, and brown sugar. Taste and adjust; keep warm over the lowest possible heat.
Preheat the broiler with a rack positioned about 6 inches from the heat source.
Combine the panko, melted butter, parsley, chives, garlic, lemon zest, and salt in a bowl until evenly moistened.
Brush the lobster meat with the melted butter and season with salt. Press the herb crust mixture firmly onto the meat.
Broil for 8 to 10 minutes, watching closely after the 6-minute mark, until the crust is deep golden and the meat reaches 140°F (60°C) internally.
Rest the lobster for 2 minutes. Spoon the warm curry sauce onto plates, set the lobster tails on top, and finish with cilantro.