Preheat your oven to 200°C/400°F. Chop and roast the hazelnuts. Stone and quarter the plums and mix with the sugar and ground cinnamon.
On a floured working surface, roll out your pie crust to 30cm/12inch and place it on a with baking paper lined baking tray. Sprinkle it with the hazelnuts, leaving a 5cm/2inch border. Starting from the middle, place the plum quarters on top of the hazelnuts. Try to arrange them in a regular pattern.
Fold the remaining dough over the filling and press slightly to seel it. Brush the crust with the egg and sprinkle with one tablespoon sugar.
Bake your plum galette for 40 minutes at 200°C/400°F in your oven. Let it cool down for 5 minutes or entirely before slicing.