Peel the garlic cloves, then slice them in half lengthwise. If desired, remove the green germ from the center of each clove for a milder flavor.
Place the garlic and kosher salt in the bowl of a food processor, preferably a smaller one for better results. Pulse several times until the garlic is finely minced, stopping occasionally to scrape down the sides of the bowl. Add the freshly squeezed lemon juice and pulse briefly to combine, ensuring an even mixture.
With the processor running, begin to drizzle in the oil slowly through the top opening. Start with about 1/4 cup of oil, then add 1 tablespoon of ice water. Pause to scrape down the sides of the bowl to ensure uniform blending.
Continue running the processor, alternating between adding the oil in a thin, steady stream and incorporating 1 tablespoon of ice water after every 1/4 cup of oil. Repeat this process until all the oil is used, and the mixture thickens and increases in volume. The finished garlic sauce should be smooth, creamy, and fluffy in texture.
This process should take approximately 10 minutes. Once done, transfer the toum to a clean container and refrigerate until ready to serve.