Pączki Donuts

Whisk together warm milk and yeast in bowl of a stand mixer until yeast softens, about 5 minutes. Add flour, egg yolks, butter, vanilla, salt, and 1/3 cup of the sugar. Beat on low speed until a dough forms, about 1 minute. Attach dough hook attachment to mixer. Beat dough on medium speed until smooth and elastic, about 8 minutes. Transfer dough to a large bowl coated with cooking spray; cover with plastic wrap and let rest in a warm (75°F) place until doubled in size, about 1 hour, 30 minutes to 2 hours.

Transfer dough to a lightly floured work surface; roll to 1/2-inch thickness. Using a 3-inch round cutter, cut out rounds of dough. Transfer rounds to a baking sheet lined with parchment paper. Gently reroll dough scraps, and repeat cutting process as needed to yield 15 dough rounds total. Cover dough rounds with plastic wrap, and let stand until almost doubled in size, about 30 minutes.

Fill a large saucepan with oil to a depth of 1 1/2 inches; heat over medium to 350°F, adjusting heat as needed to maintain temperature. Working in batches of 3, fry donuts in hot oil until golden brown, about 2 1/2 minutes per side, returning oil to 350°F between batches. Transfer cooked donuts to a baking sheet fitted with a wire rack. 

Pulse freeze-dried strawberries and 1/2 cup of the sugar in a blender until mostly smooth, 5 to 7 pulses. Transfer mixture to a medium-size shallow bowl, and stir in remaining 1/2 cup sugar. Toss warm donuts in sugar mixture, turning to coat. Return to wire rack on baking sheet. Let cool 15 minutes.

Cut a 1/2-inch-wide slit into 1 side of each donut. Place jam in a piping bag or a ziplock plastic bag with a 1/2-inch-wide hole snipped from 1 corner. Insert tip of piping bag into slit in each donut, and squeeze jam into middle of donut (you will know the donuts are adequately filled when the filling starts to push the tip of the piping bag out of the donut). Serve immediately.