Preheat the oven (210ºC thermostat 7). Melt the salted butter (careful it mustn't be too hot) and spread it on the whole surface of a baking pan. Dust the baking pan with sugar and leave a layer of about 3mm at the bottom. Add a pinch of cinnamon. Save the baking pan for later.
Peel the apples and cut them into 8 pieces. In a frying pan, melt a dessert spoon of unsalted butter with half a small glass of sugar. Add a pinch of cinnamon and let them colour. Save the cooking juice.
Elegantly line up the softened apples in the baking pan. Squeeze them a bit together to avoid the dish to collapse once it's cooked. Cover the apples with few knobs of unsalted butter, some sugar and a pinch of cinnamon. If you have some apples left, repeat this step.
Add three dessert spoons of the cooking juice on top. Put the baking pan in the oven for 20min. Take it out of the oven, let it cool for about 30min.
Cover the baking pan with the puff pastry, don't forget the edges, using a rolling pin. Put it back in the oven for 40min. If the puff pastry start to burn cover the baking pan with aluminium foil.