Combine the flour, caster sugar, instant yeast, and a pinch of salt in a mixing bowl.
In a separate bowl, whisk together lukewarm milk, egg, softened butter, and vanilla extract.
Mix the wet ingredients into the dry ingredients until a dough forms.
Knead the dough on a lightly floured surface for approximately 5 minutes until it becomes smooth and elastic.
Return the dough to the mixing bowl, cover it with a clean tea towel, and let it proof in a warm place for about 1 hour or until it doubles in size.
Once the dough has risen, roll it out on a floured surface to a thickness of about 1 cm. Use a round cutter to create donut shapes.
Heat vegetable oil in a deep frying pan to 180°C, using a kitchen thermometer to monitor the temperature.
Carefully place the doughnuts into the hot oil, frying for approximately 2-3 minutes on each side until they turn golden brown and puff up.
Remove the doughnuts from the oil and place them on a paper towel-lined plate to remove excess oil.
In a microwave-safe bowl or by using a double boiler, melt chopped dark chocolate and unsalted butter together until smooth.
You can do this in the microwave by heating in short bursts, stirring in between, until fully melted, or use a double boiler on the stovetop.
Once the chocolate and butter are melted, remove them from heat and stir in powdered sugar, whole milk, and vanilla extract until the glaze is smooth and well combined.
Adjust the glaze’s consistency by adding more milk if it’s too thick or more powdered sugar if it’s too thin.
Allow the chocolate glaze to cool slightly, ensuring it remains in a liquid state for dipping the doughnuts.
Dip each warm donut into the prepared chocolate glaze, coating one side or the top according to your preference.
Place the glazed donuts on a wire rack or a tray lined with parchment paper to allow any excess glaze to drip off.
Generously sprinkle them with colourful sprinkles.
Serve your delectable sprinkle donuts immediately.