Preheat your oven to 350°F (175°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
In a large bowl, sift together the flour, cocoa powder, baking powder, baking soda, and salt.
In another bowl, whisk together the melted butter and sugar until well combined. Beat in the eggs, one at a time, then stir in the mango puree and vanilla extract.
Gradually mix the dry ingredients into the wet mixture until just combined. Don't overmix – a few lumps are totally fine.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.