Put the flour, sugar, salt, lime zest and butter in a bowl.
Pinch the butter with the rest of the ingredients until no large lumps are left and it looks like wet sand.
Add the egg and water at the center and mix with a spatula until it doesn't help you anymore. Continue mixing with your hands but don't knead it too much or it will turn tough and it's going to be harder to stretch afterwards.
Wrap the dough in cling film and let it rest in the fridge for at least 30min. If you leave it in there longer than that and it's too cold to stretch then let it come to room temperature first.
Roll it out to 3mm thick. Don't make it thinner or it won't be able to hold the juices. Make sure that it's not sticking to the table after every stretch and add more flour to the table if necessary.
Cut the dough using a large dish.
Put the round dough on the baking tray lined with baking paper that you'll use later for baking.
Mix everything and lay at the center of the dough. Leave about 4cm of dough uncovered around the filling to fold towards the inside.
Fold the dough towards the inside to form the galette.
Mix the egg with the water and paint the dough around.
Sprinkle the sugar on top of the egg because it makes it look really nice.
Take to a preheated oven at 180C for 30-45min or until the dough is golden and the filling is bubbling.
Let it cool for 20min before cutting it.