In a small mixing bowl, combine the flour, baking powder, salt, and 4 tablespoons of milk, stirring until a ball of dough forms. If the dough feels sticky, sprinkle in a little extra flour. If it's too dry, add an additional splash of milk.
Dust your countertop with flour and roll the dough into a square about the height of your mug.
Lightly brush coconut oil over one side of the square, and then evenly dust with cane sugar and cinnamon.
Roll the dough into a log shape.
Grease the inside of your mug with the remaining coconut oil.
Place the rolled-up dough into the mug.
Microwave the mug for 50 seconds. If the dough still looks wet, continue microwaving in 5-second bursts until set.
In a different small bowl, mix the powdered sugar and milk to create the frosting. Pour it over the cinnamon bun in the mug and let it sit for about 30 seconds.
Dig in right from the mug, or transfer the cinnamon bun to a plate. It's best enjoyed while still warm.