1. Make the custard first so it can cool: whisk 3 tablespoons sugar, the cornstarch and egg yolks in a bowl. Heat 1 1/4 cups milk in a saucepan until steaming. Slowly whisk about half of the hot milk into the yolk mixture, then pour everything back into the pan.

2. Cook over medium heat, whisking constantly, until thick and bubbling, about 2 to 3 minutes. Remove from the heat and stir in 1 teaspoon vanilla and 1 tablespoon butter. Press plastic wrap onto the surface and cool completely.

3. Preheat the oven to 350°F. Grease a 9 inch springform pan and line the bottom with parchment paper.

4. Toss the sliced apples with the lemon juice, 2 tablespoons sugar and the cinnamon.

5. Whisk the flour, baking powder and salt together. In a large bowl, beat the softened butter and 2/3 cup sugar until light and creamy. Beat in the eggs one at a time, then 1 teaspoon vanilla.

6. Add the flour mixture to the butter mixture in two parts, alternating with 1/3 cup milk, and mix just until a thick batter forms. Spread the batter evenly in the pan.

7. Arrange the apple slices over the batter in overlapping circles, pressing them in lightly. Spoon the cooled custard over the apples and smooth the top, leaving a small border.

8. Unfold the puff pastry on a lightly floured surface and roll it slightly thinner. Cut it lengthwise into 4 strips. Roll or twist each strip into a rope, join the ropes end to end, and coil the long rope into a tight spiral to cover the custard.

9. Brush the pastry spiral with the egg wash.

10. Bake for 55 to 65 minutes, tenting loosely with foil after 35 minutes if the pastry browns too quickly, until the pastry is deep golden and the cake underneath is set.

11. Cool in the pan for 20 minutes, run a knife around the edge, release the springform and cool for at least 1 hour. Dust with powdered sugar before serving.