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1
Bloom the yeast: Pour the warm milk into the bowl of a stand mixer.
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2
Sprinkle the yeast on top and stir to dissolve; let stand until foamy, about 5 minutes.
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3
Make the dough: Add the sugar, salt, vanilla and eggs to the bowl and whisk until blended.
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4
Add 2 cups flour and mix with the dough hook to combine, stopping to scrape down the bowl.
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5
(The dough will be sticky; if it's too wet, add the remaining 1/4 cup flour.)
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6
Add the butter and mix until smooth.
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7
Let it rise: Brush a large bowl with vegetable oil; add the dough and cover with plastic wrap.
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8
Let rise in the refrigerator, at least 4 hours or overnight.
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9
Cut out the doughnuts: Line 2 baking sheets with parchment and dust with flour.
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10
Dust a clean surface with flour; turn out the dough onto the surface.
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11
Dust the dough with flour, then gently pat it out to make it easier to roll.
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12
Using a rolling pin, roll out the dough until about 1/2 inch thick.
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13
Cut the dough into 1 1/2-inch rounds with a cookie cutter; transfer to the prepared baking sheets.
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14
Reroll the scraps and cut out more rounds.
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15
Dust the dough rounds lightly with flour, cover with plastic wrap and let rest 1 hour in a warm place.
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16
Fry them: Heat 2 to 3 inches vegetable oil in a large pot until a deep-fry thermometer registers 360 degrees F. Working in batches, fry the doughnuts, turning, until golden brown, 1 to 1 1/2 minutes total.
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17
Using tongs or a skimmer, remove to paper towels to drain.
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18
Fill with jelly: Fit a pastry bag with a 1/8-inch-round tip; place the bag in a glass and cuff the open end over the glass.
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19
Fill the bag with jelly.
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20
Insert the pastry tip into the side of a doughnut and gently squeeze to fill.
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21
Repeat with the remaining doughnuts.
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22
Dust with confectioners' sugar and serve warm.
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23
Photograph by David A.
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