Preheat the oven to 350 degrees.
In a large bowl, mix the oat flour, almond flour, and cocoa powder.
Add the date paste, applesauce, and nondairy milk, and stir into a thick batter.
Portion 1/3 cup of batter into each lined cup - they'll be pretty full! And if you have a bit of leftover batter, just portion it evenly amongst the cupcakes (or eat it, I'm not judging).
Bake the cupcakes for 25 minutes.
While the cupcakes are baking/cooling, make the frosting by adding the chickpeas, dates, cocoa powder, and nondairy milk to a food processor.
Blend the frosting ingredients until smooth, stopping a couple times to scrape down the sides and make sure everything is totally incorporated.
Spread or pipe the frosting onto the cooled cupcakes, and enjoy!
Store leftovers in the refrigerator.