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1
Bring milk to a simmer in a 1-quart heavy saucepan, then remove from heat and stir in granulated sugar and salt. Cool milk to lukewarm (about 90u00b0F).
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2
While milk is cooling, dissolve yeast in warm water in a small bowl, stirring until creamy, then let stand until foamy, about 5 minutes. (If yeast doesn't foam, discard and start over with fresh yeast.)
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3
Pour milk mixture into a large bowl and stir in 2 1/2 cups flour, 2 tablespoons oil, eggs, and yeast mixture with a wooden spoon to make a very soft dough. Spread 1 cup flour on work surface and put dough on top, scraping it from bowl with a rubber spatula. Knead dough, incorporating all of flour from work surface and adding just enough additional flour (if necessary) to keep dough from sticking, until smooth and elastic, 5 to 8 minutes. Transfer dough to another large bowl and sprinkle lightly with additional flour, then cover bowl with a clean kitchen towel and let dough rise in a warm draft-free place until doubled in bulk, about 1 1/2 hours.
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4
Turn out dough onto a floured surface and roll out with a floured rolling pin until 1/2 inch thick. Cutout rounds with 2-inch cutter. Stretch 1 round to 2 1/2 inches and put 1 teaspoon jam in center, then stretch another round to 2 1/2 inches and use it to cover jam, pinching edges of rounds firmly together. (Pinching will stretch doughnuts to about 3 inches in diameter.) Make more jelly doughnuts in same manner.
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5
Cut through filled doughnuts with floured 21/2-inch cutter, rotating cutter several times to help seal edges. Transfer rounds to a floured kitchen towel, then reroll scraps (only once) and make more jelly doughnuts in same manner. (If dough shrinks after rerolling, let stand 10 minutes.) Cover doughnuts with another kitchen towel and let rise in a warm place 30 minutes.
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6
While doughnuts rise, heat 3 inches oil (about 10 cups) in a deep 4-quart pot until it registers 375u00b0F on thermometer. Fry doughnuts 2 at a time, turning occasionally, until puffed and golden brown, about 2 minutes per batch. (Doughnuts will bob in oil; hold them half submerged with a slotted spoon to brown evenly.) Transfer as cooked to paper towels to drain. Serve warm, dusted with confectioners sugar.
