Preheat the oven to 350 degrees F and line a 9x9 inch square pan with parchment paper.
In a medium bowl, combine the cocoa powders, chocolate, and hot coffee together. If the chocolate does not fully melt, heat in the microwave in 20 second intervals until fully melted.
In a large bowl, whisk together the flour, sugars, espresso powder, baking powder, and salt.
To the dry ingredients, add the oil, milk, yogurt, eggs and vanilla. Whisk until fully combined.
Add in the chocolate mixture and whisk until fully combined.
Pour the batter into the prepared pan and bake for 20-25 minutes or until a toothpick inserted comes out clean.
Allow cake to cool in the pan for a few minutes before removing to cool completely on a wire rack.