Mix flour, salt, cinnamon, 40g sugar, butter, water, and yeast into a smooth dough for 5 minutes.
Cover the dough and set aside for one hour to prove until doubled in size.
Divide the dough into eight portions, roll into balls, and place on a lined tray.
Let the dough balls rise in a warm place for 20 minutes.
Heat oil in a fryer to 150°C.
Deep fry dough balls in batches for 6-8 minutes until golden-brown and drain on kitchen paper.
Combine the remaining cinnamon and 75g sugar and coat the warm doughnuts.
Simmer milk, cinnamon sticks, ground cinnamon, and vanilla in a pan, then remove solids.
Whisk egg yolks and 110g sugar together until pale and fluffy.
Whisk the milk into the egg mixture, return to heat, and cook for 3 minutes until thickened.
Strain the cooled custard over whipped cream, whisk, and churn in an ice cream maker for 50 minutes.
Simmer sugar and water for 2 minutes until dissolved.
Whisk in dark chocolate until melted and smooth, then remove from heat.
Serve two doughnuts per plate with a scoop of ice cream and chocolate sauce.