For the Pesto:
In a food processor, combine all of the ingredients except for the olive oil. Pulse until coarsely chopped. With the motor running, drizzle in the olive oil. Taste with a spoon and season with more salt if needed. Several of the ingredients are salty, such as the anchovies and Pecorino, so it’s best to taste first before seasoning.
For the Grilled Branzino:
Preheat a grill or grill pan. Season the branzino with the olive oil, salt, pepper, lemon zest and rosemary. Grill skin-side down until cooked through, about 4 to 6 minutes per fillet, depending upon size.
Plate the grilled branzino fillets and top each one with a dollop of pesto. Finish with a drizzle of extra-virgin olive oil and freshly grated lemon zest. Serve immediately.