In a bowl beat the butter with the caster sugar, vanilla sugar, rum extract and salt.
Beat in the 3 egg yolks until completely incorporated. Sift in the plain and rice flour and work into the mix to create a very soft dough. Transfer the dough to a pastry bag.
Grease a 16 or 18cm tart or springform cake tin, then line with parchment.
Cut the pastry bag's tip and squeeze off the dough onto the bottom of the tin, working in a circular motion from the outer edge to the centre. Make sure that the outer-most circle also covers a bit of the side of the tin. Use 2/3 of the dough and reserve the remaining. Place both the tin and the pastry bag in the fridge while you proceed.
Prepare the filling:
In a bowl mix the ricotta with the sugar. Mix in the egg and the chestnut puree. Lightly dust the chopped chocolate in a bit of flour (so it won't sink to the bottom of the tart) and stir in.
Assemble and bake:
Remove the tin from the fridge and fill with the ricotta and chestnut mixture. Spread evenly with the back of a wet tablespoon.
Chop each marron glacé in 4 pieces and arrange over the top. Cover with the remaining shortcrust: Squeeze small rounds of dough out of the pastry bag, covering the marron glacé. Refrigerate for 20 minutes.
Preheat a fan oven to 180 C (or 200 C / Gas 6 if using a regular oven).
Remove the tart from the fridge and bake in preheated oven for 35 to 40 minutes (possibly longer if not using a fan oven). The shortcrust on top will spread and cover the entire tart. Remove from oven, cool and dust with icing sugar. Serve cool or warm.
You can also use 50g of chestnut flour in the pastry. Just reduce the plain flour to 120g and the rice flour to 100g.