Preheat oven to 350°F (175°C) and grease an 8x8-inch baking pan.
In a large bowl, whisk the hot tea and cocoa powder until smooth. Let cool slightly.
Add oil, eggs, sugar, and vanilla. Whisk until fully combined.
Stir in flour, baking soda, and salt until just combined.
Pour batter into prepared pan and bake for 28–32 minutes, or until a toothpick comes out clean.
While cake is cooling slightly, make the frosting: in a saucepan, heat cocoa powder, milk, and butter over medium heat until just bubbling.
Remove from heat and whisk in powdered sugar and vanilla until smooth.
Pour warm frosting over still-warm cake and spread evenly.
Let set for 15 minutes before slicing.