Spiced Apple Sheet Cake with Vanilla Custard Filling

Steps

1. Make the filling first so it can chill: in a saucepan whisk the whole milk, about half of the granulated sugar (50 g), the cornstarch and one of the eggs (50 g) until smooth.
2. Cook over medium heat, whisking constantly, until it bubbles, thickens and reaches 160°F (71°C), about 6 minutes. Off the heat, stir in one third of the vanilla (4 g). Press plastic wrap on the surface and chill at least 1 hour.
3. Preheat the oven to 350°F (175°C). Brush a 9x13-inch pan with a little of the melted butter and line the bottom with parchment.
4. In a bowl whisk the flour, baking powder, baking soda, salt, cinnamon and nutmeg.
5. In a large bowl whisk the rest of the melted butter, the brown sugar, the remaining granulated sugar (60 g), the remaining two eggs (100 g), the applesauce and the remaining two thirds of the vanilla (8 g) until smooth.
6. Fold the flour mixture into the applesauce mixture until just combined, then fold in the diced apple.
7. Spread half the batter in the pan. Stir the chilled custard smooth, dollop it evenly over the batter and spread gently, leaving a 1/2-inch border.
8. Drop the remaining half of the batter over the custard in spoonfuls and spread gently to cover.
9. Bake 40 to 45 minutes, until golden and a toothpick inserted in the cake (not the custard) comes out clean.
10. Cool in the pan on a rack for 1 hour, then cut into 12 slices. Refrigerate leftovers.