Preheat the oven to 350 degrees.
In a large bowl, mix the oat flour, almond flour, pumpkin pie spice and ground ginger.
Add the date paste, applesauce, molasses, and nondairy milk, and stir into a thick batter.
Portion slightly less than 1/3 cup of batter into each lined cup, and bake the cupcakes for 30 minutes.
Be sure to let the cupcakes cool in the pan for at least 30 minutes before carefully turning them out to cool completely. They're pretty soft and delicate as it is, but they'll firm up quite a bit as they cool.
To make the frosting, combine all ingredients in a food processor and blend until smooth. You'll need to stop it once to scrape down the sides and make sure everything gets incorporated.
Spread or pipe the frosting onto the cooled cupcakes and enjoy.
Store leftovers in the refrigerator.