Preheat the oven to 450 degrees F. Line a large rimmed baking sheet with parchment paper. Lay the whole snapper on the baking sheet, then score the skin with several shallow cuts on both sides. Stuff 2-3 sprigs of fresh dill and 2-3 sprigs mint into the cavity of the fish.
Mix the butter, anchovy paste, and garlic together. Rub it over the fish on all sides. Then stuff the remaining butter in the cavity. Liberally sprinkle the fish with salt and pepper.
Roast in the oven for 15-20 minutes, until the skin is crisp and the interior is opaque. In a small bowl, mix 1 tablespoon chopped dill, 1 tablespoon chopped mint, and the lemon zest together. Sprinkle over the top of the fish and serve warm!