Step 1

Preheat oven to 180°C. Grease two 22cm-diameter cake tins, line with baking paper, then grease paper and dust with flour. Beat butter, sugar and vanilla in an electric mixer fitted with the paddle attachment until pale and fluffy. Add egg, a little at a time and scraping down sides of bowl occasionally, until incorporated.

Step 2

Meanwhile, combine flour, cornflour and baking powder and sift twice. With mixer on low, add flour mixture in three batches, alternating with milk, until just combined. Turn off mixer, scrape down sides of bowl and the paddle, then beat on high for 2 seconds to aerate batter. Add grapefruit zest and juice, then stir to combine, scraping the base of the bowl to grab any butter that hasn't been incorporated. Divide batter between tins and smooth tops. Bake for 20 minutes, then reduce temperature to 140°C and bake until centre of cakes spring back when lightly pressed (5-10 minutes). Cool in tins before turning out.

Step 3

Meanwhile, combine sugar and strawberries in a heatproof bowl, tossing to coat. Wrap tightly with plastic wrap, then place over a saucepan of simmering water (don't let bowl touch water) and cook until strawberries are just starting to soften (15-20 minutes). Cool in bowl, still set over pan, but off the heat. Strain juices into a separate saucepan and reduce over medium-high heat until syrupy (1-2 minutes), then add strawberries to syrup.

Step 4

For sesame frosting, beat ingredients in an electric mixer fitted with the paddle attachment on low speed until smooth. Increase to medium speed and beat, scraping sides and base of bowl occasionally, until fluffy. Transfer to a piping bag without a nozzle.

Step 5

To assemble cake, place one sponge on a plate. Pipe over half the frosting and top with half the strawberries (avoid adding too much syrup). Sandwich with remaining sponge, and finish with remaining frosting and remaining strawberries. Drizzle with extra syrup and top with extra grapefruit zest to serve. This cake is best eaten on the day it's baked.