Sauce:
In a small saucepan, cook 2 tablespoons of the butter over moderate heat until browned and nutty-smelling, about 6 minutes.
Add the shallot and cook, stirring, for 1 minute.
Stir in the stock, lemon juice, capers and Worcestershire.
Stir in 5 tablespoons of the butter, 1 tablespoon at a time, until incorporated.
Stir in the chives. Remove the sauce from the heat and keep warm.
Fish:
Preheat the BGE to 450° using a raised grid
Grill the branzino directly over high heat, turning once, until browned, crisp, and cooked through (7 minutes per side)