Preheat oven to 170° C. Grease, then line bases and sides of two 20cm round sandwich or springform tins with baking paper.
Put butter, vanilla and sugar in the small bowl of an electric mixer and beat until pale and creamy. Add eggs, 1 at a time, beating between additions, until combined.
Transfer butter mixture to a large bowl. Sift flour and baking powder over mixture, then stir until combined. Spoon evenly into prepared tins and smooth tops. Bake for 20-25 minutes or until cakes spring back when pressed lightly in the middle. Stand cakes on a wire rack in tins for 15 minutes, then remove from tins to cool completely.
Wash and hull strawberries, then cut in quarters lengthways. Combine strawberries and jam in a small bowl. Place 1 cake on a serving plate and spread with jam mixture, then top with whipped cream. Place second cake on top and dust with icing sugar to serve.