Rinse the bulgur and rice thoroughly. Transfer them to a large pot.
Add 8 cups of water and cook over medium heat until both are very soft.
Once the mixture reaches a mushy, porridge-like texture, strain it. Then press it through a fine mesh sieve to remove the tough solids. Discard the pulp.
Let the strained mixture cool to room temperature.
In a small bowl, mix the yeast, 1 tablespoon sugar, and 1 cup lukewarm water.
Add the yeast mixture to the cooled bulgur-rice base. Whisk well to combine.
Cover the pot and let it ferment in a cool, dark place for up to 24 hours. In hot weather, 6–8 hours may be enough. Stir occasionally to let it breathe.
After fermentation, start by adding 1 cup of sugar and 6 cups of water. Mix thoroughly until smooth. Taste and add more sugar gradually if needed, mixing well after each addition. Adjust the water if necessary to achieve a thick but pourable consistency (like drinkable pudding).
Chill before serving. Pour into glasses, sprinkle with cinnamon, and garnish with roasted chickpeas if desired.
Store leftovers in the fridge and consume within a few days.