In the bowl of a food processor, pour the lukewarm milk, eggs, fine salt, lemon zest and sugar. Mix briefly with a spoon.
Sift the flour and baking powder together, pour them over the liquid mixture.
Operate the food processor fitted with the kneading hook on medium speed for 5 minutes, then faster until the dough comes away from the sides of the bowl. Then add the softened butter cut into cubes. Continue beating until it is completely incorporated.
Pour the dough into a clean bowl, cover it and let it double in volume in a warm place.
At this end, spread the dough on a lightly floured work surface and cut out 10 circles (the future donuts) to arrange them, then, on a baking sheet lined with parchment paper (make sure to space them out). Let them grow for 30 min.
Heat an oil bath to 170°C. Dip the donuts and cook for about 2 minutes. on each side. Put them on absorbent paper then coat them with sugar.
Once lukewarm or cold, using a fluted nozzle, pierce each donut on the side then stuff them with the jam.