Preheat the oven to 350°F (175°C). Grease an 8-inch round pan and line the bottom with parchment paper.
In a large bowl, whisk together the flour, cocoa powder, baking powder, baking soda, sugar, and salt.
Add the egg, milk, melted butter, oil, and vanilla. Whisk until smooth.
Slowly whisk in the boiling water. The batter will be thin.
Pour into the prepared pan and bake for 38 to 42 minutes, until the center is set and a toothpick comes out with moist crumbs.
Cool in the pan for 10 minutes. Turn the cake out onto a serving plate and let it rest for another 10 minutes.
For the sauce, place the chocolate in a heatproof bowl.
Heat the heavy cream until steaming. Pour it over the chocolate and let it sit for 3 to 5 minutes.
Stir until glossy and smooth. Let the sauce stand for 15 minutes to thicken slightly.
Serve warm slices with vanilla ice cream and warm fudge sauce.