Preheat the oven to 350°F (175°C). Grease and line your cake tins with baking paper. You can use three 6-inch (15 cm) round pans or two 8-inch (20 cm) pans. This recipe uses three 6-inch pans for a taller, layered cake.
In a large mixing bowl, whisk together the milk, vinegar, and yogurt. Let the mixture sit for about 5 minutes to curdle slightly, creating a buttermilk-like texture.
Add castor sugar, light brown sugar, oil, and vanilla extract. Mix until sugars dissolve and the mixture is smooth.
Sift cocoa powder, baking powder, baking soda, flour, and salt into the wet mixture. Gently fold until smooth and lump-free, without overmixing.
Evenly divide the batter between the prepared cake tins. Bake for 20–22 minutes, or until the tops are set and a toothpick inserted into the center comes out clean.
Let the cakes cool in the tins for 5–10 minutes, then transfer them to a wire rack to cool completely.
Once cooled, trim a thin layer off the top of each cake to level them before assembling.