Preheat the oven to 350°F and lightly brush a 0.5qt mini Dutch oven (or a 5" ramekin/cake pan) with butter.
In a bowl, whisk together the oil, yogurt, and 2 tbsp boiling water until combined. Whisk in the sugar.
Sift in the flour, cocoa powder, baking powder, baking soda, and salt. Gently fold until just combined.
Pour the batter into the prepared pan.
In a separate bowl, stir together the granulated sugar, brown sugar, and cocoa powder for the hot fudge until no lumps remain. Sprinkle this mixture over the cake batter.
Carefully pour the ⅓ cup of boiling water on top of the sugar and cocoa mixture.
Transfer the pan to the preheated oven and bake for about 20 minutes until the cake looks done on top. Aim for slight underbaking to ensure a gooey fudge sauce.
Serve the cake warm straight from the pan! Optionally, top with a scoop of plain cold whipped cream or ice cream.