1. Cook the strawberry filling by simmering strawberries, sugar, lemon juice, and zest with water until the berries soften.

2. Stir cornstarch into a little cold water, add to the strawberries, and cook until thick and glossy. Cool completely, then chill.

3. Preheat the oven to 350°F (175°C). Grease and line three 8- or 9-inch round cake pans with parchment, then lightly flour the sides.

4. Whisk flour, baking powder, baking soda, and salt together in a medium bowl.

5. In a large bowl, beat butter, oil, and sugar until pale and fluffy.

6. Add eggs one at a time, mixing well, then blend in vanilla, lemon zest, and lemon juice.

7. Add dry ingredients in 2–3 additions, alternating with buttermilk, beginning and ending with dry ingredients. Mix just until combined.

8. Divide batter evenly among prepared pans, smooth the tops, and bake 22–26 minutes, or until a toothpick comes out clean.

9. Cool cakes in pans for 10 minutes, then turn out onto wire racks to cool completely. For neater layers, wrap and chill the cakes.

10. For the frosting, beat cream cheese and butter until smooth.

11. Gradually add powdered sugar, then mix in lemon juice, lemon zest, vanilla, and enough cream to reach a fluffy, spreadable consistency.

12. Place one cake layer on a serving plate, spread a thin layer of frosting, then add a layer of chilled strawberry filling, staying slightly inside the edge.

13. Repeat with the second cake layer, frosting, and more filling, then top with the final cake layer.

14. Frost the top and sides of the cake with remaining frosting, smoothing or leaving it semi-naked as desired.

15. Chill the cake 30–45 minutes to set the layers. Garnish with fresh strawberries, lemon slices, mint, and a dusting of powdered sugar before serving.