Activate the Yeast: In a small bowl, dissolve the yeast and a pinch of sugar in the warm water. Let it sit for about 5-10 minutes until frothy.
Prepare the Dough: In a large mixing bowl, combine the warm milk and sugar. Stir until the sugar is dissolved. Add the activated yeast mixture and 1 cup of flour. Mix until well combined. Cover the bowl with a clean kitchen towel and let it rest in a warm place for about 30 minutes, or until the mixture is bubbly and doubled in size.
Add Eggs and Butter: Once the mixture has risen, add the eggs, softened butter, salt, and vanilla extract. Gradually add the remaining flour, about 1/2 cup at a time, until a soft dough forms.
Knead the Dough: Turn the dough out onto a floured surface and knead it for about 5-7 minutes until smooth and elastic. Add more flour if necessary to prevent sticking. Shape the dough into a ball.
Let the Dough Rise: Place the dough ball in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1-2 hours, or until doubled in size.
Roll and Cut the Dough: Once the dough has risen, punch it down and transfer it to a floured surface. Roll the dough out to about 1/2 inch thickness. Using a round cookie cutter or drinking glass, cut out circles of dough. Re-roll any scraps and continue cutting until all the dough is used.
Proof the Donuts: Place the dough circles on a lightly floured baking sheet, cover with a clean kitchen towel, and let them proof in a warm place for about 30-45 minutes, or until they are puffed up and nearly doubled in size.
Fry the Donuts: In a large, deep pot or Dutch oven, heat avocado oil or vegetable oil to 350°F (180°C). Carefully add a few donuts to the hot oil, being careful not to overcrowd the pot. Fry for 1-2 minutes on each side, or until golden brown and puffed. Remove the fried donuts with a slotted spoon and drain them on a paper towel-lined plate. Repeat with the remaining dough circles.
Fill the Donuts: Once the donuts have cooled slightly, use a piping bag fitted with a round tip to fill them with jam or jelly of your choice. Insert the tip into the side of each donut and squeeze gently until filled.
Coat with Sugar: Roll the filled donuts in granulated sugar to coat them evenly. Alternatively, you can dust them with powdered sugar for a different finish.
Serve: Sufganiyot are best served fresh and warm. Enjoy your delicious homemade Israeli donuts as a festive treat during Hanukkah or any time of year!
Note: Be careful when working with hot oil, and always supervise children around hot cooking surfaces.