Preheat oven to 350 degrees F (175 degrees C). Grease a 9x12-inch baking pan with cooking spray and dust with rice flour.
Combine rice flour, brown sugar, salt, baking soda, and cocoa powder in a food processor; pulse until well mixed. Mix in olive oil. Pour in garbanzo beans with liquid; puree until smooth. Blend in water gradually. Mix in vinegar; batter will be thin. Pour batter into the prepared baking pan.
Bake in the preheated oven until edges pull away from the pan, 45 to 50 minutes. Cool for 1 hour before serving, otherwise it will be crumbly.
