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1
Put the garlic in a mortar with the sea salt and pound it into a paste with a pestle; you can also do this with a knife, mincing and then smooshing the garlic and salt into a paste with the side of the blade. However you do it, work until you have a completely smooth -- not chunky -- paste.
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2
Transfer the garlic paste into a food processor. Add the egg yolks, pimenton, and vinegar and pulse to mix. With the machine running, begin to add the olive oil in a slow, steady stream. After you've added about a third of the oil, the mixture will start to come together. Add 2 tablespoons of the water to thin the aioli and prevent it from breaking. Continue to add the oil. As the mixture thickens up again, add the remaining 2 tablespoons water, a little at a time, just as needed to correct the consistency. Once all of the oil has been added, turn off the machine and taste the aioli. Add salt if you need it.
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3
Note: You can also make this by hand; that's how I like to do it. Here's how: Combine the garlic paste, pimenton aioli, yolk, and vinegar in a sturdy mixing bowl. (Steady yourself with a tea towel underneath the bowl to avoid slippage.) Whisk them to combine. Then start adding the oil, just a drop at a time, and whisk furiously. After you've added about a quarter cup, the mixture will start to emulsify, and you can add the oil in a steady stream, but don't get crazy. Skip the water, unless your aioli is just too thick to handle; it's more likely to break the emulsion when you make your aioli by hand.
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4
The aioli will keep, covered tightly in the refrigerator, for up to 1 week.
