How to Make It
Preheat oven to 425°F. Line a rimmed baking sheet with parchment paper. Set aside.
Process parsley, shallot, garlic, thyme, lemon zest, and red pepper in a food processor until finely chopped, about 15 seconds. Add oil, and process until well incorporated, about 15 seconds. Toss together potatoes, onion wedges, 2 tablespoons of the parsley mixture, and 1 teaspoon of the salt in a large bowl.
Cut 3 (2-inch-long) slits diagonally on both sides of fish, cutting all the way to the bone on both sides. Rub exterior and inside of cuts with 1 cup of the parsley mixture and remaining 1 3/4 teaspoons salt; place fish on prepared baking sheet. Spread potato mixture around fish. Bake in preheated oven until fish is opaque and flaky and vegetables are tender, about 30 minutes.
Drizzle fish with remaining 1/4 cup parsley mixture. Serve with lemon wedges.