Split each clove lengthwise, and remove the germ, especially any green stuff.
Pulse garlic and salt in a food processor until finely minced. Frequently scrape down the sides with a flexible spatula. This takes about 2 minutes of processing, and the scraping should be done every 20 seconds.
Add 1 tbsp lemon juice, and pulse until a paste begins to form.
Add another tbsp lemon juice and keep pulsing until completely smooth.
With the processor on medium-high speed, slowly drizzle 1 cup of oil, followed by 1 tbsp lemon juice. Repeat until everything is combined. Do not stop the food processor during these steps. Processing the oil should take 15-20 minutes.