Peel the garlic cloves. Halve them and remove any green germ if desired.
Place the garlic and salt in a small food processor. Pulse until finely minced, scraping down the bowl as needed.
Add the lemon juice and pulse to combine.
With the processor running on low, drizzle in the oil extremely slowly. After approximately each 1/4 cup of oil, add about 1 tablespoon of ice water and scrape down the bowl.
Continue alternating oil and ice water until all the oil has been incorporated and the sauce is smooth, fluffy, and increased in volume, about 10 minutes.
Taste and adjust with additional salt or lemon juice if needed.
Notes
Do not rush the emulsification; adding the oil too quickly may cause the sauce to split.
A small food processor works best for this quantity.
Store refrigerated in a tightly sealed container for up to 4 weeks, or freeze portions for later use.