How to Make It
In a medium bowl, dissolve the yeast in the water. Mix in the flour. Cover with plastic and let rise in a warm place until doubled in bulk, 1 hour.
In a standing mixer fitted with the dough hook, dissolve the yeast in the milk. Add the flour, salt, egg yolks, butter, sugar and the starter and mix until the dough forms a ball. Scrape the dough into a bowl, cover and let rise in a warm place until doubled in bulk, 1 hour.
In a saucepan, simmer the raspberries with the 1 1/2 cups of sugar over moderate heat until thickened, about 25 minutes. Scrape the jam into a bowl and let cool for 1 hour.
Line a baking sheet with parchment paper. On a floured work surface, roll out the dough 1/2 inch thick. Stamp out 1-inch round doughnuts as close together as possible. Reroll the scraps and stamp out more doughnuts. Transfer the rounds to the baking sheet and cover with a damp cloth. Let stand for 15 minutes.
In a saucepan, heat 1 inch of oil to 325°. Fry the doughnuts until golden, 2 minutes. Drain, then roll the doughnuts in sugar. Serve hot, with the raspberry jam.