Preheat the oven to 450 degrees F. Remove the leaves from 2 sage sprigs, 1 parsley sprig, all of the thyme sprigs and the rosemary; finely chop along with the lemon zest. Transfer to a small bowl and stir in the garlic and 1 tablespoon olive oil to make a paste; set aside.
Brush a rimmed baking sheet with olive oil. Run the back of a knife over the skin of the fish to remove any excess moisture; pat dry inside and out. Transfer to the prepared baking sheet. Cut 4 slits through the skin on each side of the fish with a sharp knife; rub inside and out with 1 tablespoon olive oil, making sure to get inside the slits. Season the fish inside and out with 1 1/2 teaspoons salt and 1/2 teaspoon pepper; spread the herb paste all over the inside.
Roast until a thermometer inserted into the thickest part reaches 130 degrees F to 135 degrees F, 15 to 20 minutes. Remove from the oven and let rest 5 minutes before slicing.
Meanwhile, heat the remaining 2 tablespoons olive oil in a small skillet over medium-high heat. Remove the leaves from the remaining 1 sage sprig and 2 parsley sprigs; add to the hot oil and cook, stirring, until crisp, 30 seconds to 1 minute. Drain on paper towels and season with salt.