Preheat the oven to gas 6/200°C/fan 180°C.
Melt 50g butter and 50g caster sugar in an ovenproof frying pan over a medium heat.
Add the cinnamon stick and swirl the pan around until the mixture transforms into a golden caramel.
Place pears snugly in the pan so they cover its base.
Cook gently over medium-low heat for 10 mins or until softened slightly.
Remove from the heat and discard the cinnamon stick.
Leave to cool.
Unroll puff pastry.
Cut out a circle 2cm wider than the pan.
Carefully place over the pears, pressing down the sides to ensure the pastry goes to the edge.
Prick all over with a fork.
Brush with beaten egg, then bake for 20-30 mins or until puffed up and golden.
Cool for 5-10 mins in the pan
Run a sharp knife between the pastry and the edge.
Place a plate over the top of the pan.
Invert pan to release tarte tartin.