Smash the garlic with the salt on a cutting board using the side of a large, heavy knife (or mash with a mortar and pestle). Continue to crush the salt into the garlic until it becomes a paste.
Combine the garlic paste mayonnaise, lemon zest and juice, and parsley in a bowl and whisk to combine. Cover and refrigerate until ready to use. (The aioli will last for up to a few days in an ai