Preheat the oven to 350°F (175°C). Grease the sides of an 8" (20 cm) round cake pan and line the bottom with parchment paper.
In a medium mixing bowl, mix together the flour, cocoa powder, baking powder, and salt. Set aside.
1 cup + 2 tablespoons (141 grams) flour, 1/2 cup (58 grams) Dutch-process cocoa powder, 2 teaspoons baking powder, 1/4 teaspoon salt
In a large mixing bowl, mix together the remaining ingredients (eggs through vanilla). It's okay if the mixture starts to separate. It'll come together after you add the dry ingredients.
2 large eggs, 1 cup (200 grams) granulated sugar, 1/2 cup (113 grams) refined coconut oil, 1 teaspoon vanilla extract
Add the dry mixture to the wet and stir just until combined. It'll likely be very thick and sticky.
Pour the batter in the prepared pan and bake for 14 minutes or a toothpick inserted in the very edge of the cake comes out clean. (A toothpick inserted in the middle will come out wet.) The edges should be crisp and the middle still moist and sticky. It'll look underbaked but it won't be totally liquidy.
Let the cake cool for 10 minutes in the pan, and then run a paring knife around the edge of the pan.
Invert the cake onto a serving plate and remove the parchment paper (if using a springform pan, no need to invert). If you made the gluten-free version, it may be a little gritty while still warm. Let it cool and the grittiness will go away.
Serve warm, room temperature, or cold. Store in an airtight container for up to 2 days or refrigerate for 5 days.