Bring half a liter of water to a boil and pour it over the almonds. Let them sit until the water is lukewarm (about half an hour).
Squeeze the almonds out of their skins (optional) and place them in a food processor or blender. Add 300 ml of water. Finely grind the almonds; this takes a few minutes in a food processor, whereas a blender should finish the job in 30 seconds. Let the mixture rest for 5 to 15 minutes.
Line a pot with a cheesecloth and pour the mixture into it. Squeeze all the liquid out through the cloth; this liquid is the almond milk. The almond pulp remaining in the cloth can be used for other purposes, though not in this recipe.
Cut the white bread into small cubes—as small as possible (to remain authentic). Alternatively, you can simply process the bread into crumbs using a food processor.
Bring the almond milk to a boil while stirring. Then add the bread. Simmer for 5 minutes. Spoon the mixture into small bowls. Sprinkle with sugar before serving.