Prepare an 8 x 8 inch (20 x 20 cm) square baking pan with parchement paper and heat the oven to 350° F (180° C.) Measure out the flour, baking powder, and salt into a bowl, stir them together, and set aside.
In a large bowl, with a hand mixer, a spoon, or your hands, mix together the coconut oil and sugar. Some brands of coconut oil can be lumpier than others, so you may have to mix with your hands to get all of the lumps out.
Once the oil and sugar are combined into a crumbly mixture, add the egg and mix again. The batter should all come together at this point, and should be mostly free of lumps.
Add half the flour mixture and stir until just combined, then add the coconut milk and mix until it is also incorporated. Add the second half of the flour and scrape the sides of the bowl to make sure everything gets in, and mix one final time. Avoid overmixing.
Pour the batter into the baking pan and bake until the cake is about 7/8 of the way done, 30-35 minutes.