Preheat oven to 356F (180C).
Prepare the baking tins: 1 with a diameter of 20cm (7.87 inch), or 2-3 with a diameter of 16-18cm (6.30-7.09 inch); line with parchment or grease with butter and sprinkle with flour.
- Sift the flour, baking soda and salt. Set aside.
- Beat soft butter with sugar until fluffy, for at least 5-7 minutes.
- Pour in vegetable oil, and beat again.
- Add the eggs one at a time, beating each time until smooth.
- Add vanilla extract, and beat.
- Pour half of the butter.
- Then add all the dry ingredients in batches while continuing to beat.
- At the end, mix in the rest of the buttermilk with a spatula.
- Pour the batter into the baking tins.
- Bake in the preheated oven at 356F (180C) for 35 minutes if there are two tins, or at least 40 minutes if you have one large. Check the readiness wit a skewer. It should come out dry from the center.
- Cool the spoge on a wire rack. If desired, cut each sponge into 2 parts (or into three if you have just on big sponge).
- Beat the butter with powdered sugar until fluffy.
- Add the cold cream cheese, and beat.
- Pour in the cream, and beat again.
Apply the cream on each sponge cake, and layer with strawberry slices.