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1
Make the aioli: finely chop the dill and garlic, and crush in a mortar and pestle, or with a spoon. Mix with the egg yolk and lemon juice. Whisking constantly, or stirring constantly in the mortar and pestle, add the oils a drop at a time. You can add them in a thin stream once the aioli begins to thicken. When you have added all the olive oil, taste and add more dill, lemon, or garlic, and salt to taste.
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2
If you have a grill, skip to step 4. If you are using a broiler, you may need to preheat your oven first depending on the method of broiling. My broiler is below my oven and they can't be on at the same time, so I preheated the oven before broiling. In any case, your oven should be at about 350 before you begin broiling. Line a pan with tinfoil and place the swordfish in it.
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3
Coat the top and sides of the swordfish with aioli, like you are frosting a cake (though it doesn't have to be as thick). Broil, aioli side up, for a minute or two until the aioli is scorched and bubbling. Remove from broiler, flip, and coat the other side with aioli. Broil for another few minutes and then transfer to 350 oven for 5-10 minutes, or until cooked through. Serve any extra aioli sauce from the pan with the fish.
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4
If you are grilling, coat the swordfish with aioli as described above and grill, turning after a few minutes. You may need to baste with the aioli while it grills and before you turn it. Continue until cooked through, about 5-10 minutes depending on your grill.
