Preheat oven to 400° F. Line a large rimmed baking sheet with parchment. Arrange mackerel, skin side up, on baking sheet. Season mackerel with salt and pepper and drizzle with 1 tablespoon olive oil. Roast mackerel 12 to 15 minutes, or until skin crisps and fish flakes easily when pierced with a fork.
Meanwhile, set a steamer basket over 1-inch of boiling salted water in a medium saucepan. Place potatoes in basket and steam, covered, until potatoes are tender, 12 to 15 minutes. Transfer steamed potatoes to a large bowl with 1 tablespoon olive oil, 1 teaspoon sherry vinegar and parsley leaves. Season potatoes with salt and pepper.
Place egg yolks, garlic and paprika in a blender; season with salt and pepper. With motor running, pour remaining olive oil into blender jar in a thin, steady stream. Stir in remaining 2 teaspoons sherry vinegar. Serve allioli with mackerel and potatoes.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.