Start by placing the peeled garlic cloves into your food processor. Add the kosher salt. Pulse until the garlic is finely minced, scraping down the sides of the bowl as needed.
With the food processor running, slowly drizzle in the vegetable oil. It’s important to do this gradually to allow the mixture to emulsify properly.
Once the oil is fully incorporated, add the freshly squeezed lemon juice. Then, while the processor is still running, add the ice water in a slow stream.
After everything is well combined, taste your sauce. You can adjust the seasoning by adding more salt or lemon juice according to your preference.
Transfer the garlic sauce to a storage container. If you’re serving it immediately, consider drizzling some extra virgin olive oil on top and garnishing with fresh chopped parsley.