Make the espresso cake

Cup of Yum
1. Preheat the oven to 350°F (176°C) and position a rack in the center of the oven. Butter and flour a 10- to 12-cup Bundt pan or fluted tube pan and tap out the excess flour.
2. Combine the brewed coffee and espresso powder in a glass measuring cup and let cool.
3. Sift the flour, baking powder, and salt together in a bowl.
4. Beat the butter in the bowl of a heavy-duty stand mixer fitted with the paddle attachment on high speed until smooth, about 1 minute. Gradually beat in the sugar, then add the vanilla and beat, scraping the sides of the bowl occasionally, until the mixture is very light in color and texture, about 4 minutes. Beat in the egg yolks, 1 at a time.
5. Reduce the mixer speed to low. Add the flour mixture in 3 additions, alternating with the cooled coffee in 2 additions, beginning and ending with the flour mixture. Beat until smooth after each addition.
6. Beat the egg whites in a bowl with a handheld electric mixer on high speed or a balloon whisk until soft peaks form. Using a spatula, stir about 1/4 of the egg whites into the batter, then gently fold in the remaining whites. Scrape the batter into the prepared pan. Smooth the top with the spatula.
7. Bake until the top of the cake springs back when gently pressed with your finger and a cake tester inserted into the center of the cake comes out clean, 45 to 60 minutes.
8. Cool the cake on a wire rack for 10 minutes. Invert and unmold the cake onto the wire rack set over a baking sheet. Cool completely.

Make the coffee glaze

1. In a small saucepan off the stovetop, stir the brewed coffee and espresso powder until the espresso powder dissolves. Stir in the milk. Add the confectioners sugar and whisk until smooth. Place over low heat and heat, whisking constantly, until the glaze is warm to the touch and thins slightly.

Glaze the cake

1. Transfer the glaze to a glass measuring cup. Slowly pour the warm glaze over the cake, letting it flow over the indentations in the cake down the center of the cake. You will have plenty of glaze. (This is a good thing!) Cool completely before slicing. (The cake can be stored at room temperature, wrapped in plastic wrap, for up to 2 days.)