Step 1

Preheat oven to 425°F. Line a rimmed baking sheet with parchment paper. Set aside.

Step 2

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.

Step 3

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.

Step 4

Drizzle fish with remaining 1/4 cup parsley mixture. Serve with lemon wedges.