1) Bring milk to a simmer in a 1 litre heavy saucepan, then remove from heat and stir in sugar and salt. Pour into a large bowl and let cool slightly.
2) While milk is cooling, dissolve yeast in warm water in a small bowl, stirring. Let stand for 5 minutes.
3) Stir the yeast mixture into the milk, along with 30ml of oil, eggs, and zest. Stir in 375g flour with a wooden spoon to make a very soft dough.
4) Spread 150g flour on work surface and put dough on top, scraping it from bowl with a rubber spatula. Knead dough, incorporating all of flour from work surface and adding just enough additional flour (if necessary), about 5 minutes; dough should be slightly sticky. Transfer dough to an oiled large bowl and sprinkle lightly with additional flour. Cover bowl with a clean kitchen towel and let dough rise in a warm draft-free place until doubled in bulk, about 1 1/2 hours.
5) Turn out dough onto a floured surface and roll out with a floured rolling pin until 2.5-cm thick. Cut out rounds with a 5-cm cutter. Place on a baking tray and cover doughnuts with another kitchen towel and let rise in a warm place for 30 minutes.
6) While doughnuts rise, heat oil in a deep 4 litre pot until it registers 185 degrees C on a thermometer. Fry doughnuts 2 at a time, turning once or twice, until puffed and golden brown, about 2 to 3 minutes per batch. Transfer to paper towels to drain.
7) Place jam in a pastry bag fitted with a 2.5-cm plain tip and poke the tip into the center of each doughnut (entering from the side) and squeeze in some of the jam.
8) Ice the top with some of the ganache and sprinkle with hazelnuts; serve.
For the ganache:
1) Bring cream to a simmer in a small saucepan. Place white chocolate in a large bowl, pour hot cream over, and let sit for 1 minute; whisk until smooth.
2) Let cool until slightly thickened.