This smoky aioli is the base of Saltie's Scuttlebutt sandwich, but you'll also want to keep a jar on hand at all times for any smearing and dunking needs that may arise. For a snack, try it dabbed on hard-boiled eggs.
Note: If you use a food processor, you may want to add a bit of water, midway through adding your oil, to thin it out. If make the aioli by hand, don't add the water! It's more likely to break that way.
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.
Transfer the garlic paste into a food processor. Add the egg yolks, pimentón, 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.
Note: You can also make this by hand; that's how I like to do it. Here's how: Combine the garlic paste, pimentón 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.
The aioli will keep, covered tightly in the refrigerator, for up to 1 week.