Grease a rectangular tart tin (approx. 20 x 28 cm) with a removable base. Knead the flour, 60 g sugar, 1 pinch of salt, 1 egg and 125 g butter in pieces first with the dough hooks of the hand mixer and then briefly with your hands to a smooth dough.
Roll out the shortcrust pastry on some flour to a rectangle (approx. 24 x 32 cm). Line a tart tin with it and press the edges into the grooves. Prick the pastry base several times with a fork, chill for about 1 hour.
Cut out a rectangle (approx. 24 x 32 cm) from baking paper, place it on the dough and fill the dried peas onto the paper. Pre-bake in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: level 3) for approx. 20 minutes.
Remove dry peas together with baking paper and continue baking the tart for about 5 minutes. Let it cool down in the tin.
Cut the lady fingers into pieces (approx. 1.5 cm). Chop the chocolate and melt in a hot water bath with 75 g butter. Let cool for about 5 minutes. Beat 4 eggs and 1 pinch of salt with the whisk of the hand mixer for about 1 minute until frothy.
While continuing to beat, add 75 g sugar and continue beating for 2-3 minutes.
Stir the butter-chocolate mixture and crème fraîche into the egg foam one after the other. Fold in the lady fingers. Fill into the tart and smooth it down. Continue baking at the same temperature for about 45 minutes.
Leave to cool in the tart mould on a cake rack. Remove from the mould and dust with icing sugar.