Preheat the oven to 160C (320F). Line the bottoms and sides of two 6 inch (15 cm) cake pans with parchment paper.
In a bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, or in a mixing bowl with a hand mixer, beat the sugar, butter, and vanilla on medium-high for five minutes until well combined.
Add the oil and beat until the mixture turns pale yellow and fluffy. Add the melted chocolate and mix until incorporated.
Add the egg and beat until the mixture looks smooth and emulsified.
Add half of the dry ingredients and mix just until combined. Add the milk and mix again. Add the remaining dry ingredients and mix until no dry spots remain and the batter looks smooth.
Divide the batter evenly between the pans. Bake for 27–30 minutes, or until a toothpick inserted in the center comes out clean.
Let the cakes cool in the pans until safe to handle, then invert them onto a cooling rack. Cool until just warm.
Wrap each layer in plastic wrap and refrigerate until completely chilled.