Peel the cloves of 1 head of garlic. Pulse in a food processor with 1 teaspoon of kosher salt until finely minced, scraping down the sides. Add the juice of 1 lemon and pulse to a paste.
With the motor running, drizzle in 1¾ cups of neutral oil very slowly, alternating with 6 tablespoons of ice water, a tablespoon at a time. Process for about 10 minutes in total, until thick, white and fluffy.