Inspired by tortilla Española, this version of the classic Spanish dish uses mild, sweet leeks instead of onions. The addition of paprika-seasoned cod adds unexpected bites of smoky flavor, and cutting the potatoes into small cubes allows the tortilla to cook faster. The leek- and garlic-infused cooking oil is used to make a flavorful aioli to accompany the omelet. Store leftover flavored oil in the fridge and use it to make salad dressings, to sauté greens or fry eggs.
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In a 10-inch nonstick skillet, heat oil over medium until shimmering. (A potato dropped into the oil should sizzle.) Add potatoes, leeks and 2 teaspoons of the garlic and cook, stirring occasionally, until potatoes are tender in the center and golden in spots, about 15 minutes. The mixture should be at a brisk simmer and completely submerged in the oil. (After a few minutes, the vegetables will soften and shrink.) Set a strainer over a heatproof bowl and drain the potato mixture; reserve the infused cooking oil. Wipe out the skillet.
While the potato mixture cooks, combine cod and paprika in a small bowl; season with salt and pepper, and mix well.
Once the potato mixture is drained, beat the eggs in a large bowl. Add potato mixture, season with salt and pepper, and mix until well blended; fold in cod.
In the skillet, heat 2 tablespoons of the reserved oil over medium-low. Add the egg mixture and cook, using a spatula to pull in the set edges and allow liquid to flow out, about 2 minutes. Cook until eggs are set around the edges but still slightly runny in the center, about 3 minutes longer.
Using oven mitts or kitchen towels and a plate that is larger than the skillet, place the plate over the skillet and carefully flip the skillet to invert the tortilla onto the plate. Heat 2 tablespoons of the reserved oil in the skillet over medium and slide the tortilla back into the skillet, cooked side up. Cook until golden underneath and center is just set, 2 to 3 minutes longer. Slide out the tortilla onto a serving platter.
While the tortilla cooks, combine mayonnaise, the remaining 1 teaspoon garlic, ¼ cup of the reserved cooking oil and 1 tablespoon of water and season with salt; stir aioli until smooth.
Cut tortilla into wedges and top with some of the aioli. Serve with remaining aioli on the side.
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