Melt vegan butter or vegetable ghee in a small saucepan on medium heat.
Add chickpea flour and mix evenly with a spatula or wooden spoon to form a crumbly mixture.
Stir continuously (to prevent scorching) until butter starts to seep out of the mixture, creating a paste that resembles thick peanut butter. This step can take a while so don't get impatient! Your first sign that the mixture is almost there is when it starts getting darker in places.
Turn off the heat and mix in the powdered sugar and cardamom. Once thoroughly combined, take the saucepan off the heat.
When it has cooled enough to handle, take handfuls of the mixture and roll with your palms into ping pong-sized balls. Let cool fully (see Note 3).
Notes
If you don't have pre-ground cardamom powder, you can also use a blender or mortar and pestle to grind up whole green cardamom pods into cardamom powder. Note that it doesn't have to be super uniform and fine.
If you prefer less sweetness, you can start with 1/2 cup of powdered sugar and add more to taste.
Cooling the ladoos is optional, but the inner texture is different when eaten warm (like a chewy peanut butter cookie) vs room temperature (crumbly and "fall apart" in your mouth). Try both and see which you prefer!