Mix the butter with the sugar, lemon zest, and vanilla extract until it gets light and creamy. Use a stand mixer with a paddle attachment or a handheld mixer.
Add the eggs one at a time, mixing well after each addition.
Sift the flour with the baking powder and add to the batter. Mix until completely combined.
Wrap ¾ of the dough in plastic wrap and place in the fridge for 30 minutes or until firm.
Roll out the remaining ¼ of the dough between two sheets of parchment paper or between a Silpat and a parchment paper. Roll the dough to ¼ inch thickness. Place it on a tray and take it to the freezer.
While the dough cools, make the filling. Place the quince with the water in a saucepan and bring it to medium-low heat. Smash with a fork until a paste is formed. If your quince already has a spreadable texture, you may skip this step.
Once cold, take the large dough, and break it with your hands, knead lightly. Roll with a rolling pin and place on the mold. Press the sides and remove the excess dough.
Pour the filling over the dough and spread neatly.
For the dough strips, remove the other dough from the freezer, and peel off the papers or the silicone sheet. Cut 8 strips with a knife and a ruler. Place the strips on the pie in a lattice design.
Cut little leaves or flowers with the rest of the dough, and place them around the pie, sticking them with a little water or milk.
Bake the pie in a preheated oven at 340°F (170°C) for 35 minutes, until the edges and strips are golden brown. Let cool for at least two hours before unmolding and serving.