In a small food processor, pulse garlic and salt together, pausing every few pulses to scrape down the sides of the bowl. Continue to pulse for several minutes until a rough paste is formed. Add lemon juice and pulse again to combine. Continue to scrape down sides. Garlic should be smooth at this point.
With the food processor running, very slowly add in the oil in a thin steady stream- about 1/4 cup of oil at a time. Do not rush or the mixture will break, or turn very runny. You’re looking for a thickened white sauce. After 1/2 cup is added, pour in the cold water while the food processor is on, and continue slowly adding the oil. This can take up to 10 minutes (seriously), so be patient.
If your mixture is thin (mine was the first time I tried it!), you can still save it using an egg white method that technically makes it not a traditional toum, but still delicious. To fix it, in an immersion blender or another small food processor, whip 1 large egg white and slowly pour in 1/4 cup of the broken sauce. Continue to run the food processor until the sauce is thick and white. Then, slowly pour in the remaining broken sauce with the food processor running until the entire batch is thick, fluffy and white.