Combine the sugar, yeast, flour, and salt in the bowl of a stand mixer and whisk. Add in the milk and the yolks and continue mixing, using the hook attachment on medium-low speed. Then add the butter, increasing the speed to medium-high. Mix until the dough is smooth and elastic.
Coat a large bowl with oil. Form the dough into a ball, place in the bowl, and coat with oil. Cover with plastic wrap or a damp towel and let rise in a warm place until it has doubled in size after about 1 to 1 1/2 hours.
Grab a baking sheet and lightly flour it. Punch down the dough, transfer to a lightly floured work surface and roll it out until it's about 1/4-inch thick. Using a 2-inch round cutter, stamp out as many balls of dough as possible and place on the lightly floured baking sheet about 1/2-inch apart. You should end up with about 30. Cover loosely with plastic and let rise for about 30 minutes.
In a large, heavy-bottomed pot, put your canola or vegetable oil and set over medium heat until the oil reaches 350 degrees on a candy thermometer. Meanwhile, line a second baking sheet with paper towels and place a wire rack over the paper towels. Place your jam in a piping bag with a 1/4-inch round tip.
Using a flat spatula, transfer the doughnuts into the oil. Fry until the bottoms are golden brown. Flip with a fork to fry the second side. Remove with a slotted spoon and transfer to wire rack.
When cooled, use a paring knife to puncture the side of each to form a center pocket. Place the tip of the piping bag into the pocket, squeezing in about 1 teaspoon of jelly or jam. Dust with powdered sugar.