Soak the bread. Tear the stale white bread into chunks and submerge in cold water for 10 minutes. It should absorb the water fully.
Squeeze completely dry. Lift the soaked bread and squeeze with both hands until no more water can be extracted. This step is not optional — excess water prevents the emulsion from forming. The squeezed bread should feel dense and almost rubbery, not wet.
Pound the garlic. In a mortar, combine the garlic cloves and salt. Pound steadily until you have a completely smooth paste. The salt acts as an abrasive and helps break down the cell structure. If you do not have a mortar, crush the garlic on a cutting board using the flat of a knife with salt underneath.
Combine and emulsify. In a food processor (or continuing in the mortar), work the garlic paste into the squeezed bread until the mixture is uniform. With the machine running — or while stirring vigorously — add the olive oil in a slow, thin, steady stream. Alternate every 2–3 tablespoons of oil with a splash of lemon juice. Continue until all the oil is incorporated and the mixture is pale, thick, and smooth.
Adjust consistency and season. If the skordalia is too thick, add cold water one tablespoon at a time. Taste and adjust with salt and lemon juice. The flavor should be intensely garlicky with a clean, bright finish.