Preheat oven to 350F. Line the bottom of a 9-in cake pan with a parchment paper round and lightly grease bottom and sides. Set aside.
In a large bowl, whisk sugar, oil, egg, milk, coffee, and vanilla until smooth. Add flour, cocoa, baking soda, baking powder, and salt to liquid and gently fold until just combined (batter will be slightly thin)
Scrape batter into prepared pan. Bake cake at 350F 28-30 minute or until cake comes out with moist crumbs sticking to it. Cool cake completely on a wire cooling rack then, invert onto a serving plate.
Make the frosting: In a small saucepan, whisk sugar, cocoa, cornstarch, and salt with water until smooth. Bring mixture to a boil over medium heat until frosting is thickened and smooth. Remove from heat and whisk in butter and vanilla.
Allow frosting to cool slightly, then frost over cooled cake. Slice and enjoy!