In a large bowl, dissolve yeast in warm milk. Add 2 cups flour; mix well. Let stand in a warm place for 30 minutes. Add the egg yolks, egg, sugar, salt, lemon zest and vanilla; mix well. Beat in butter and remaining flour. Do not knead. Cover and let rise in a warm place until doubled, about 45 minutes.
Punch dough down. On a lightly floured surface, roll out to 1/2-in. thickness. Cut with a 2-1/2-in. biscuit cutter. Place on lightly greased baking sheets. Cover and let rise until nearly doubled, about 35 minutes.
In a deep-fat fryer or electric skillet, heat oil to 375°. Fry doughnuts, a few at a time, for 1-1/2 to 2 minutes on each side or until browned. Drain on paper towels.
Cool for 2-3 minutes; cut a small slit with a sharp knife on one side of each doughnut. Cut a small hole in the corner of a pastry bag; insert a very small round tip. Fill bag with jelly. Fill each doughnut with about 1 teaspoon jelly. Carefully roll warm doughnuts in sugar. Serve warm.
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