Place garlic and salt in the food processor. Process until completely smooth, stopping frequently to scrape down the sides. The garlic must become a fine, creamy paste with no visible chunks.
With the processor running, add oil one teaspoon at a time. This slow start is essential. The mixture will begin to thicken and turn pale. Rushing this step will cause separation.
Once the emulsion forms, continue adding oil in a thin stream, alternating occasionally with small amounts of lemon juice. This balance keeps the sauce stable and prevents it from becoming greasy.
Continue blending until the toum becomes fluffy, white, and holds shape. Taste and adjust salt or lemon carefully. The sauce should be intense but clean.