Preheat the oven to 350°F. Grease and flour a 9 x 13-inch pan or a 10 x 15-inch jelly roll pan; set aside.
In a large bowl, whisk together the flour, sugar, baking soda, and salt; set aside.
In a medium saucepan, bring the water, butter, cocoa powder, and espresso powder to a boil, stirring constantly. Pour the hot mixture over the dry ingredients and whisk together until smooth. In a separate bowl, whisk together the yogurt, buttermilk, eggs, and vanilla. Pour the buttermilk mixture into the cake batter and whisk until smooth.
Scrape the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, about 20-25 minutes.
For the Frosting
Meanwhile, in a medium saucepan melt the butter over medium heat. Remove from the heat and add the cocoa powder, buttermilk, confectioners' sugar, and vanilla, whisking until smooth. Return to low heat and cook, stirring occasionally, for 5 minutes. Pour the warm frosting over the warm cake, spreading evenly with an offset spatula. Allow the cake to cool completely before serving. Enjoy!
Notes
Cake can be covered and stored at room temperature for up to 3 days.