Preheat oven to 350°F (177°C). Line an 8 x 8 inch square baking pan with parchment paper.
Add flour and cocoa powder to a large mixing bowl. Mix on low speed with a mixer until evenly combined and there are no clumps of flour or cocoa powder. Add in sugar and mix on low speed until combined. Pour in water and oil and mix batter (medium to high speed) until it is smooth. See notes if you wish to mix the batter by hand.
Pour batter into the prepared cake pan. Bake for about 30 minutes or until cake is done and toothpick inserted comes out clean. Let cake cool completely before frosting and cutting.
Notes
The batter can be mixed by hand, but you need to whisk the dry ingredients very well and break up any cocoa or flour lumps before adding the liquid, otherwise you won't be able to whisk them out of the batter.
To make your own self-rising flour, combine 1 and 1/2 cups all purpose flour, 2 and 1/4 teaspoons baking powder and 3/8 tsp salt. Whisk until thoroughly and evenly combined.
If you want an even deeper chocolate flavor, you can use 1/2 cup of cocoa powder in the cake instead of 1/3 cup. The cake will not be as sweet though and will have a dark chocolate flavor.
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You can use whatever chocolate frosting you prefer or don't frost the cake at all.
To make the frosting I used in the pictures, you will need 4 tbsp melted coconut oil, 1/2 cup cacao powder or natural cocoa powder (dutch process will not work), and 4 tbsp pure maple syrup. First mix the coconut oil and cocoa powder and until smooth. Then add in the maple syrup (which will thicken your frosting), and whisk until smooth. This frosting is not that sweet but has a very rich chocolate flavor. You can add an extra tablespoon of maple syrup to make it sweeter, but adding too much will change the consistency.
The nutrition information provided are only estimates based on an online nutritional calculator. This is not a comprehensive list of all the nutrients in the recipe (i.e., does not include vitamins, cholesterol, etc). I am not a certified nutritionist. Please consult a nutritionist or doctor for accurate information and any dietary restrictions and concerns you may have.