Process the garlic. Smash the garlic with the side of your knife, then remove the peels. Optionally, remove the green germ from the center as you go (it can be bitter). Place the peeled garlic and kosher salt in the small bowl of a food processor. Pulse a few times until the garlic looks minced, stopping to scrape down the sides.
Add the lemon juice and pulse a few times to combine, again scraping down the sides.
Slowly incorporate the oil. With the food processor on low speed, drizzle in the oil in ever so slowly through the opening at the top. After you've used about ¼ cup or so, add in about 1 tablespoon of the ice water. Stop to scrape down the sides of the processor bowl.
Finish, adjust the seasoning, and serve. Keep the processor running and continue to slowly drizzle in the oil, adding a tablespoon of the ice water after every ¼ cup of oil. Continue on with this process until you have used up the oil entirely. The garlic sauce has thickened and increased in volume (it should look smooth and fluffy). This should take somewhere around 10 minutes or so. Taste and adjust the seasoning with more salt and or lemon juice if necessary. Enjoy!
