Quickly knead flour, 1 egg, 1 pinch of salt, 60 g sugar and butter in flakes with the dough hooks of the hand mixer to a smooth dough. Wrap in foil and chill for about 30 minutes. In the meantime, wash the limes and grate them dry. Grate the zest of 3 limes and squeeze the juice. Mix cream cheese, crème fraîche, 250 g sugar, lime juice and zest, 5 eggs, pudding powder and semolina. Roll out the shortcrust pastry on a floured work surface until round (32 cm Ø). Line a greased and floured springform pan (26 cm Ø) with the shortcrust pastry, pressing the edges down.
Pour in the cream cheese mixture and smooth it down. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for 50-60 minutes. Cover after 40 minutes if necessary. Remove the cake from the oven. Remove from the edge of the springform pan with a knife and let it cool down for about 2 1/2 hours. Before serving, brush the rim with sugar syrup and sprinkle with brown sugar. Cut 1 lime into thin slices and decorate the cake with them