Set your oven to 350°F (180°C). Line a 9×13 inch baking pan with parchment paper.
In a large bowl, beat the softened butter and sugar until pale and creamy. This takes 2 to 3 minutes with a hand mixer.
½ cup unsalted butter, ½ cup caster sugar
Beat in the eggs, Greek yogurt, vanilla, and salt. Mix until combined.
2 large eggs, 2 tsp vanilla extract, ½ cup Greek yogurt, ½ tsp salt
In a separate bowl, whisk the flour, baking powder, and baking soda. Add the dry mix to the wet mix in two additions. Stir until just combined.
1¾ cups all-purpose flour, 1 tsp baking powder, ½ tsp baking soda
Spread the batter into the lined pan. Bake for 18 to 22 minutes. Mine was done at 18 minutes. The sponge is ready when a toothpick in the center comes out clean and the edges are golden.
Leave the sponge in the pan for 10 minutes, then lift it onto a wire rack to cool fully.
While the cake cools, put the berries in a small saucepan over medium heat. Cook for 5 to 7 minutes until they break down and release their juices. Blend smooth, then strain through a sieve to remove seeds. Let it cool.
10½ oz fresh or frozen red berries
Beat the cream cheese, Greek yogurt, and powdered sugar for 10 to 20 seconds until smooth.
8 oz cream cheese, ⅔ cup Greek yogurt, 2 tbsp powdered sugar
Cut the cooled sponge into 16-20 squares. Pipe or spoon the cream cheese topping onto each square. Add a small spoonful of berry sauce and top with half a strawberry.
9 oz fresh strawberries
Notes
Check the sponge at 16 minutes. Ovens vary, and this cake dries out quickly if overbaked. Store assembled cakes in the fridge for up to 2 days.You can also bake the sponge in a larger, shallower sheet pan for thinner cake squares. The batter will spread more thinly, so start checking for doneness earlier than the recommended baking time. The exact time will depend on the pan size and depth.