Preheat the oven to 425°F.
Heat the oil in a large saucepan and sauté the garlic, saffron and paprika until fragrant, about 1 minute. Stir in the rice and toast in the oil, stirring, until opaque.
Add 4 cups of water and salt and bring to a boil. Turn the heat to low and simmer for 20 to 25 minutes, until tender.
Toss the artichoke hearts on a baking sheet with 1 tablespoon of oil and a pinch of salt and pepper. Roast for 10 to 15 minutes, until crisp.
Stir the peas, roasted artichokes and piquillo peppers into the rice in the last 3 minutes of cooking.
Place the branzini on a baking sheet, drizzle with olive oil and sprinkle liberally with salt and pepper, including the cavity.
Heat a large ovenproof or other skillet over high heat. Add the branzino and cook for 3 minutes per side, until the skin is crisp. Transfer to the oven (using a baking sheet if you don't have an ovenproof skillet) and roast for 10 minutes, until cooked through.
To make the chimichurri, add all ingredients except the oil to a blender. Purée until smooth. With the motor running, drizzle in the oil until emulsified. Season to taste.
To serve, divide the rice and branzino between plates. Top with chimichurri and serve with a lemon wedge on the side.