Begin by setting your oven to 350°F (175°C). Prepare two round cake pans by greasing them well and dusting lightly with flour. This will help the cakes release easily after baking.
In a large bowl, mix together the flour, cocoa powder, sugar, baking powder, baking soda, and salt. Stir until everything is evenly blended.
Add the eggs, milk, oil, vanilla, and espresso powder to the dry ingredients. Mix until the batter looks smooth and uniform, with no lumps.
Slowly stir in the boiling water. Don’t worry if the batter seems very thin — that’s exactly how it should be for a tender, moist cake.
Pour the batter evenly into the prepared pans. Place them in the oven and bake for 30 to 35 minutes, checking for doneness by inserting a toothpick into the center. If it comes out clean, the cakes are ready. Remove from the oven and allow them to cool completely.
For the boiled icing, place the sugar, corn syrup, water, cream of tartar, and salt in a saucepan. Cook over medium heat, stirring gently until the sugar dissolves and the mixture becomes hot.
In a separate heatproof bowl, beat the egg whites until soft peaks form. While beating, slowly drizzle the hot sugar syrup into the egg whites. Keep beating until the icing thickens, becomes glossy, and cools down. Add the vanilla and mix gently.
To finish, place one cake layer on a plate or cake stand. Spread icing over the top, then place the second layer on top. Frost the entire cake with the remaining icing, smoothing it over the top and sides.