Mix flour, yeast and sugar in the bowl of an electric mixer fitted with a dough hook to combine. Add warm milk, cream, butter, egg, cinnamon and a pinch of salt, and mix until a smooth dough forms. Cover bowl with a damp tea towel and stand in a warm place until doubled in size (1 hour).
For raspberry jam, combine raspberries, sugar, lemon juice, vanilla seeds and 80ml water in a saucepan over low-medium heat and gently stir occasionally until a syrup forms and deepens in colour (30-40 minutes). Strain through a fine sieve, pressing the seeds to extract as much liquid as possible. You should have 300ml. Return the liquid with 1 tbsp seeds (discard remainder) to a clean pan over medium-high heat and bring to the simmer. Add the cornflour mixture and bring to the boil, stirring continuously. Remove from heat, transfer to a container and set aside to cool.
Turn dough out onto a floured bench, knock back and flatten to 1cm thickness, then cut into 6cm rounds with a cutter and place on a tray to prove further (5-10 minutes).
Heat oil in a deep saucepan to 175C. Deep-fry doughnuts in batches, turning occasionally, until golden and puffed (3-4 minutes on each side – take care, hot oil will spit), then drain on absorbent paper. Roll in caster sugar, then, while still warm, pierce a hole in one end and pipe raspberry mixture into the centre. Serve warm.
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