Preheat oven to 350˚F. Grease and line 9x9 inch pan with parchment paper.
In a medium bowl, mix together 1½ cups flour, ½ cup cocoa, 1 teaspoon baking powder, 1 teaspoon baking soda, ½ teaspoon salt and 1 teaspoon espresso powder.
In a medium bowl soften ⅓ cup butter and add 1½ cups sugar . Whisk well. Add 1 egg and 1 teaspoon vanilla, and whisk again.
In a measuring cup, add 1 Tablespoon vinegar to ¾ cup milk. Add to egg mixture.
Pour liquid ingredients into dry ingredients. Mix together. Add ¾ cup boiling water to mixture and blend with a whisk until well combined. The batter will be thin.
Pour into prepared pan.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center of the cake comes out clean. Cool on a wire rack. Frost as desired.