Preheat the oven to 350°F and grease a 9-inch cake pan.
In a mixing bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, cream together sugar and butter until light and fluffy.
Beat in the eggs, one at a time, until well combined.
In a small bowl, dissolve the espresso powder in boiling water and add it to the butter mixture.
Stir in the vanilla extract.
Gradually add the dry ingredients to the wet mixture and mix until well combined.
Pour the batter into the prepared cake pan and bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Let the cake cool for 10 minutes before removing it from the pan and transferring it to a wire rack to cool completely.