Mix the warm milk, sugar, and yeast in a bowl. Add 2-3 spoonfuls of sifted flour and stir well until the yeast fully dissolves. Leave the mixture (sponge) in a warm place to activate the yeast. Once the sponge has expanded and formed bubbles, add the egg, vanilla, and half of the butter, mixing well.
Sift most of the flour and pour the sponge into it, stirring thoroughly. Once the dough is no longer extremely sticky, transfer it to a floured work surface and begin kneading. Gradually add the remaining flour and vegetable oil. It is crucial to ensure the dough remains light and fluffy without becoming overworked or heavy with flour. Knead for about 10 more minutes.
(If you have a planetary mixer, you can let it take on the heavy task of kneading the dough for you.)
Next, place the dough in an oil-greased bowl, cover it with cling film, and leave it in the fridge overnight for a slow fermentation process.
In the morning, punch down the dough, transfer it to a floured work surface, and roll it out to a 1-1.5 cm thickness. Use a glass to cut out circles 6-7 cm in diameter.
Allow the circles to prove for another 20 minutes, then fry them in hot oil on both sides until golden and fluffy.
Place the sufganiyot on paper towels. While still warm, fill them with jam and dust the tops with icing sugar.
Filling:
Mash the thawed apricots and coat them with sugar.
Place them in a heavy-bottomed saucepan and simmer over low heat until thickened. Blend the mixture until smooth and homogeneous. Add ground cardamom and stir well. If the jam is not thick enough, mix a little starch with water and pour it into the jam. Heat it again until the starch thickens the mixture.
In 30 ml of hot water, dissolve the saffron entirely and then pour the mixture into the jam.
Allow the jam to cool and leave it in the fridge overnight to let all the flavours blend.