Pour 2 C. dairy-free milk into a medium saucepan and whisk in the sugar. Bring to a simmer and stir until sugar is dissolved.
In a small bowl whisk together the chickpea flour, additional ½ C. dairy-free milk and tapioca starch until thoroughly blended. Drizzle into the warmed milk and stir until thickened, keeping on low-medium heat. This mixture will continue to thicken as it cools, so don’t worry if it doesn't look too thick.
Remove from heat and pour into a glass bowl, then stir in the vanilla. Top with plastic wrap to prevent skin from forming. Put in refrigerator to chill, or put aside to cool down.