Place the garlic paste and egg yolk in a chilled stainless steel or glass mixing bowl.

Whisk the egg yolk and garlic together until combined and slightly pale.

Add the lemon juice and salt, whisking until the salt has dissolved.

While whisking vigorously, begin adding the olive oil drop by drop to ensure a stable emulsion forms.

Once the mixture begins to thicken and emulsify, increase the oil flow to a very thin, steady stream while continuing to whisk constantly.

If the emulsion becomes too thick, whisk in the warm water to adjust the consistency.

Continue whisking until all oil is incorporated and the aioli is smooth and creamy.

Cover and refrigerate for at least 30 minutes before serving to allow flavors to meld.