Heat the oven to 180°C/350°F and grease and line a 20cm/8-inch springform pan.
Chop half the apples into 1/2-inch pieces and slice the remaining half about 1/8 inch thick.
Put the chopped and sliced apples in separate bowls. Divide the melted apple butter, white sugar, and cinnamon between them, toss to coat, and set aside.
Whisk the flour, baking powder, and salt in a large bowl.
In a separate bowl, whisk the melted batter butter, oil, eggs, sugar, and vanilla until combined.
Pour the wet mixture into the dry ingredients and stir with a wooden spoon or rubber spatula until the flour is incorporated.
Fold in the chopped apples gently, just until dispersed.
Scrape the batter into the pan and smooth the surface. Fan the sliced apples over the top in overlapping circles.
Bake for about 50 minutes, until a skewer inserted in the centre comes out clean. Cover loosely with foil if the apples brown before the cake is done.
Set the pan on a cooling rack and release the springform sides.
Warm the apricot jam and water for 20 seconds, stir, and brush the glaze over the apples.
Cool for at least 30 minutes before slicing; serve slightly warm or at room temperature.