Use a mortar and pestle to grind together the mahlab seeds and cardamom seeds.
To make the galette pastry, use a food processor and add in the cold butter, ground mahlab and cardamom, flour, icing sugar and pulse until the mixture resembles fine breadcrumbs. Then proceed with the egg yolk and water until your mixture turns moist, coarser breadcrumbs. You know it's ready when you press it together, it should hold together.
Empty the dough in a clean working surface and bring it together, without kneading. Share the dough in four balls and flatten into disks. Cover in plastic wrap and let rest in the fridge for 30-40 minutes.
Prepare the fruit, slicing them thinly. Place them in a large bowl along with the lemon and sugar and toss to cover.
Preheat the oven at 180 C. Line your tray with a baking sheet.
Take the cool dough out of the fridge and grab your rolling pin. Roll out each disk into 17-18 cm rounds of roughly 5mm thickness. Move it to the lined baking tray and repeat with the rest of the dough.
Divide the quince and apple filling in the middle of the pastry and leave about 3 cm space from the edge. Fold in the edges to wrap the filling and return in the fridge for another 10 minutes.
While you wait, mix the egg and water to combine and brush over the pastries with the egg wash and sprinkle the sugar on top each disc.
Bake in the middle rack for 15-20 minutes – until the pastry turns golden.