Start by making the dough. In a small bowl whisk together the flour, baking powder, salt and 4 tbsp of vegan milk. Mix until you get a dough ball. You can add a little bit more flour if it is stick, or a little bit more milk, if it seems dry.
Put some flour on the surface of your counter and roll out the dough in a square, about the height of your mug.
Brush some coconut oil on one side and then sprinkle the sugar and cinnamon over the dough. Roll up the dough.
Brush the remaining coconut oil on the inside of your mug. Place the rolled dough in the mug.
Put the mug in the microwave for 50 seconds. If it seems too wet, you can add a few more seconds (in increments of 5 seconds), until no longer wet.
In a separate small bowl mix together the frosting ingredients, the powdered sugar and vegan milk, and pour this over the cinnamon bun in the mug, and let it sit for 30 seconds before serving.