In a large bowl, whisk together the all-purpose flour, granulated sugar, cocoa powder, baking soda, baking powder, and salt until well combined with no lumps of cocoa remaining.
In a separate bowl, whisk the egg, buttermilk, warm water, vegetable oil, and vanilla extract until smooth. Pour the wet ingredients into the dry ingredients and stir until just combined into a smooth, thin batter. Do not overmix.
Spray a 6-inch round cake pan with nonstick cooking spray and line the bottom with a circle of parchment paper for easy removal. Pour the batter into the prepared pan.
Preheat the air fryer to 310 degrees F. Carefully place the cake pan into the air fryer basket. Cook for 25 to 30 minutes, until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Remove the pan from the air fryer and let the cake cool in the pan for 10 minutes. Then turn it out onto a wire rack to cool completely before adding the ganache.
While the cake cools, prepare the chocolate ganache. Place the finely chopped semi-sweet chocolate in a heatproof bowl. Heat the heavy cream in a small saucepan until it just begins to simmer, then pour it over the chocolate. Let it sit for 1 minute, then add the butter and stir slowly from the center outward until completely smooth and glossy.
Place the cooled cake on a serving plate and pour the ganache over the top, letting it drip down the sides naturally. Allow the ganache to set for about 15 minutes before slicing and serving.