Line a 6-cup or standard 12-cup muffin pan with paper liners.
In a medium bowl, whisk together the flour, cocoa powder, potato starch, arrowroot, baking powder, baking soda, and xanthan gum.
Add maple syrup, hot water, applesauce, and vanilla. Stir until the batter is smooth, adding hot water as needed.
Pour 1/3 cup batter into each prepared cup, almost filling it.
Bake the cupcakes on the center rack for 20 minutes, rotating the pan 180 degrees after 15 minutes. The finished cupcakes will bounce back when pressure is applied gently to the center.
Let the cupcakes stand in the pan for 20 minutes, then transfer them to a wire rack and cool completely.
Creamy Chocolate Frosting
Add all ingredients to food processor and blend until smooth.
Spread frosting over cooled cupcakes.
Transfer to a refrigerator to set for an hour before serving.