Preheat the oven to 350f. Line and grease 2x6 inch round cake pans.
Sift together the flour baking powder and salt. Set aside. In a measuring cup dissolve the espresso powder in the boiling water and set aside to cool.
In a mixer fitted with the paddle, beat the butter until soft and creamy. About 2 minutes. Gradually add the sugar and continue to beat until pale and very fluffy. Scrape the sides to the bowl down once or twice while mixing, to ensure that the sugar is incorporated evenly. Then beat in the vanilla.
Beat the eggs in one at a time, scraping down after each addition, allowing each egg to be incorporated before continuing. Add the flour mixture in 4 additions alternately with the milk. Begin and end with the flour mixture, and beat briefly until smooth on medium-low speed after each addition. Gently mix the cooled espresso into the cake batter.
Divide the batter evenly between the two pans and smooth the tops with a spatula. Place the cakes in the middle of the oven and bake for about 20 minutes, until a toothpick shows a few moist crumbs. The cake will be pale golden around the edges and the top and will have started to pull away from the sides of the pan.
Leave to cool in the pan for 5 minutes. Then turn out onto a wire rack. Peel off the parchment paper and leave until fully cooled. About 1 hour.