In a medium bowl, dissolve the arrowroot into the coconut milk. Set aside.
Pour the ¾ cup of water into a medium saucepan. Add the agar and boil.
Once it boils, turn heat to low and whisk every now and then for four minutes.
Add the coconut nectar syrup, salt, and cocoa powder until well combined. Allow to boil while remembering to whisk constantly.
Slowly add the arrowroot and the coconut milk mixture. Again, whisk until smooth.
Let the mixture simmer over low heat while stirring constantly. Remove from heat when a pudding-like texture is achieved.
Add the coconut oil, vanilla, and the chocolate chips. Mix well until smooth. Place in a bowl and let it cool at room temperature. Once cool, cover it with plastic wrap and put in the fridge overnight.
Preheat the oven to 350 degrees Fahrenheit and place paper liners in 16 muffin cups.
In a bowl, sift the baking powder, salt, baking soda, and flour. Set aside.
Puree the avocado in a food processor until smooth.
In a saucepan, pour coconut milk and dissolve the cocoa powder. Whisk constantly over moderate heat until it starts to bubble. Add the cocoa and coconut milk mixture to the pureed avocados in the food processor, including the coconut nectar syrup, vanilla, and coconut oil. Puree until smooth.
Pour the avocado and cocoa mixture into the bowl of dry ingredients. Mix well.
Scoop the cupcake batter into the muffin cups. Fill each of them about 2/3 full.
Bake for 25 mins. Leave the cupcakes in the muffin pan for 15 mins. before transferring into a cooling rack.
Take the chilled frosting out of the fridge and put into a food processor. Process until it becomes spreadable and smooth.