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Arrange 2 shelves in the oven at a fair distance from each other.
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The foil-enveloped fish will need some room to puff and expand as it cooks.
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Better to rearrange the oven racks while the oven is not yet hot.
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Preheat the oven to 400 degrees F.
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Bake the potato until tender, about 45 minutes to 1 hour.
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Spread about a 2-foot sheet of foil on a flat surface with 1/2 of it hanging off the counter in front of you.
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Put the fish, skin side down, horizontally, onto the foil near the end of the counter leaving about 1 1/2-inches of foil on both sides.
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Season the flesh side of the fish with salt and pepper, to taste, and sprinkle with some dill, parsley and a few lemon slices.
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Drizzle about 2 tablespoons oil on top of the fish.
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Fold the foil back over the fish and fold in the sides of the foil twice.
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Leaving some air in the package, roll the top of the foil down twice gathering the top to make a window , leaving about 6 to 8 inches between the fish and the top.
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It should look like a small package, with all the sides sealed.
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There should be enough room left around the fish to allow for the steam to build up as it cooks, creating an inflated envelope around the fish.
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Repeat with remaining 3 pieces of fish.
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Put the garlic cloves in the bowl of a food processor and pulse until the garlic is finely chopped.
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Add the egg yolks and pulse to blend.
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When the potato is completely cooked and still warm, put it on a flat surface and split it open lengthwise.
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Use a tablespoon to scoop out the flesh, totaling about 3 to 4 tablespoons, and add it to the processor.
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Pulse to combine.
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With the processor running, slowly add the 1/2 cup of olive oil, through the opening at the top, in a steady stream.
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Add the sugar and the lime juice and pulse to incorporate.
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Season, to taste, with salt and pepper.
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Cook s Note: If the mixture is too thick, add a little cold water to loosen the texture.
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Transfer the mixture to a serving bowl, cover and refrigerate.
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25
Using 2 baking sheets, put 2 of the foil envelopes on each sheet and add a little water to the bottom of the sheet pan.
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This water will create additional steam in the oven as the fish cooks.
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Put the baking sheets on 2 shelves of the oven and bake, undisturbed, until the envelopes begin to puff, about 12 to 15 minutes.
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Remove from the oven and immediately transfer to 4 dinner plates.
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To serve, break open the foil and drizzle with the aioli.
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Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness.
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To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.