Preheat the oven to 170°C. Prepare three small baking pans (diameter of 18 cm) with baking paper. If you have only 2 or 1 rotate them in the oven until there is no batter left.
In a bowl whip the butter, oil and sugars until creamy. Now listen - make sure you cream these ingredients for at least 8 minutes or more. The mixture should get very creamy and light in colour.
Add eggs, and mix again. Make sure you take time and let the mixture get twice its size. Scrape the bowl in the middle of the process.
In another bowl mix flour, and baking powder. Pour milk into the glass with lemon juice. Add ⅓ of the flour mix and whisk on slow speed. Pour ½ of the milk and whisk on slow speed as well. Continue in the process until you add the flour mix last.
Crush half of the Oreo into smaller and bigger pieces. Add them to the batter and fold them in with a rubber spatula.
Divide the batter evenly between the baking pans. Bake for 35-45 minutes or until the toothpick comes out clean. Take the cakes out of the oven and let cool completely.