Tarte Tatin

On a recent trip to France I got the chance to eat a home mage Tarte Tatin - which is similar to an upside down apple cake but I felt that the ratio of apples to dough was more to my liking ( = more apples).

Upon my return I searched for a recipe and found this one that I adapted a bit since I don't have a pan that can go into the oven.

Ingredients
Apples, peeled, cored and quartered
Lemon juice
100g sugar
2/3 stick butter, cubed
2 tsp cinnamon
Pinch of allspice
3 tbsp calvados
Puff pastry, rolled out in a circle shape a bit larger than the baking dish.
Egg yolk with a bit of water

Mix apples with lemon juice.
Add sugar to a pot and heat on medium heat until the sugar caramelizes.
Then add butter, cinnamon, and allspice.
When the butter is melted, and the mixture boils, add calvados and cook for another 2 minutes.
Add the apples, then cover and let cook on low for 10 minutes.
Get a baking dish ready. Add the apple mixture and cover with puff pastry.
Brush the egg yolk onto the dough. Bake for ~30 minutes.

When I took the cake out of the oven, I let it stand for a little bit before I turned it over, to let the liquid settle.