Stir yeast and 60ml warm water in a bowl to combine, then set aside until mixture begins to foam (5-7 minutes). Mix flour, sugar, milk, butter, egg, 1 tsp fine sea salt and yeast mixture in an electric mixer fitted with a dough hook on low speed to combine and knead until a sticky dough forms (4-5 minutes). Transfer to a buttered bowl, cover with plastic wrap and stand in a warm place until doubled in size (1-1½ hours).
Turn dough out onto a floured surface and roll out to 1.5cm thick. Cut out rounds with a floured 8cm-diameter cutter, then cut out holes with a 2cm-diameter cutter. Place 2cm apart on trays lined with baking paper, cover and set aside until doubled in size (45 minutes to 1 hour). Reroll scraps and repeat.
Meanwhile, melt chocolate in a heatproof bowl over a saucepan of simmering water, stirring occasionally, until smooth. Remove from heat, add crème fraîche and cream, and whisk until soft peaks form (2-3 minutes). Refrigerate until just firm (20-30 minutes), then transfer to a piping bag fitted with a plain nozzle.
For milk chocolate glaze, stir sugar and 60ml water in a saucepan over medium-high heat until sugar dissolves, then bring to the boil and cook until dark caramel (4-5 minutes). Remove from heat, add 100ml water (be careful, hot caramel will spit), swirl to combine, then add chocolate and return to heat and whisk until smooth. Remove from heat and keep warm.
Heat oil in a large, deep saucepan or deep-fryer to 180C. Deep-fry doughnuts in batches, turning occasionally, until light golden and cooked through (2-3 minutes; be careful, hot oil will spit). Drain on paper towels and cool slightly, then halve horizontally. Dip tops in glaze to coat and place on a tray to set.
To serve, pipe a little chocolate cream over doughnut bases, sandwich with glazed doughnut tops, scatter with crumbled biscuits and serve.