In a bowl, mix warm milk, sugar, and yeast. Let sit for 5 minutes until foamy. Add the egg, flour, and salt, and knead for about 10 minutes until smooth. Add softened butter and knead again until the dough is soft, elastic, and slightly shiny.

Cover and let rise in a warm place for 1–2 hours, or until doubled in size.

Divide the dough into 8 equal pieces (about 60–70 g each) and roll into smooth balls. Place each on a small square of baking paper, this makes it easy to transfer them into the oil without losing their shape. Cover loosely and let rise again for 30 minutes until light and puffy.

Heat oil to 160°C (320°F) and fry the bomboloni (with the baking paper underneath, it will detach after a few seconds). Fry for about 2–3 minutes per side, until golden brown. Drain on paper towels and roll in sugar while still warm.

Heat the milk until almost boiling. In a separate bowl, whisk together egg yolks, sugar, and cornstarch until smooth. Slowly add some hot milk while whisking, then return everything to the saucepan. Cook over medium heat, stirring constantly, until thickened. Remove from heat, then add dark cocoa drops and butter. Stir until smooth and glossy. Cover with plastic wrap and chill for at least 4 hours. Once chilled, whip the cold cream to stiff peaks and gently fold it into the chocolate custard until fully combined. If the filling feels too watery after combining with the whipping cream put it in the fridge for 2-3 hours.

Transfer the cream into a piping bag and inject into each bombolone until it feels soft and full.