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Grease a large mixing bowl, set off to the side.
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In a large liquid measuring cup, combine eggs, milk, yolk, and vanilla.
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In the bowl of an electric stand mixer fitted with the paddle attachment, mix the flour, yeast, sugar, salt on low until combined. Add the room temperature butter. Mix on low until no pieces of butter are visible. Add the cold butter and mix on low until the butter pieces are no larger than 1/2 an inch.
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Add the milk mixture. Mix on low until a very sticky and lumpy dough forms. Use a spatula and scrape the dough into the prepared bowl. Cover with plastic wrap and let rise in the refrigerator overnight.
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The next morning, transfer dough to well floured surface. Knead the dough about 10 times by hand and form into a ball. Dust lightly with flour and cover with a tea towel. Let the dough come to room temperature.
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Press the dough into a 6x6-inch square. Use flour as needed if the dough gets too sticky. Roll the dough out into a 16x20 inch rectangle. Sprinkle more flour if it gets too sticky.
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Use a bench scraper to fold the short ends of the rectangle in on the middle section to make three layers of folded dough. This is the first turn.
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Flip the dough over seam side down and roll into a 8x16-inch rectangle. Do the same thing as before, use a bench scraper to fold the short ends in on the middle section to make three layers. Flip the dough seam side down and repeat this step two more times.
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After the fourth time, just gently press down the dough with a rolling pin and cut in half width wise. Cover each half of the dough with plastic wrap and chill for one hour.
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Work with one half of dough at a time. Place the chilled dough on a well floured work surface. Roll out into a 10x14-inch rectangle, flour as needed so dough doesn't stick. Trim any rough edges. Cut the dough vertically into 8 even pieces.
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Hold one end of the dough strip in place with one hand and twist the other end of the strip into a spiral with your other hand. Tuck one end under itself and pinch to seal then curl the spiral into a snail shape. Tuck the loose end underneath the snail. Gently pinch into the dough so it won't come loose during baking. Continue until all 8 snails are made. Place the prepared danishes on a large baking sheet lined with parchment paper.
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Let the danishes rise for an hour and a half.
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Continue this snail making process with the other half of the dough.
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Preheat the oven to 350 degrees F.
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Brush the danishes with the egg wash.
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Use two fingers to gently create a well in the center of each danish. Place a scant teaspoon of the jam into the well of each danish.
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Bake for 18-20 minutes until golden brown.
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Transfer to wire baking sheet to cool.
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While the danishes cool, make the glaze. Whisk the sugar, milk, and vanilla together. Use the whisk to drizzle the glaze over the tops of each danish.
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