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1
Make the dough: Place the milk in a small saucepan. Split the vanilla bean in half and scrape the seeds out into the saucepan. Add the scraped, split pod to the pan, too. Warm the milk over medium heat, bringing it just under a boil. When you see little bubbles around the rim and the milk is steaming, remove the pan from the heat and let the milk cool to lukewarm.
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2
Pour the warm water into the bowl of a stand mixer fitted with the dough hook (or a large bowl); sprinkle in the yeast and stir to dissolve.
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3
Add the lukewarm milk, sugar, salt, eggs, 1 cup of the flour, and the cardamom and mix together on low speed. Add the butter and mix to combine. Beat in 2 cups of the flour until the mixture is smooth. Add enough of the remaining flour to form a supersoft dough. Knead it in the mixer with the dough hook, or turn it out onto a work surface dusted with flour and knead it by hand for 3 to 4 minutes, until the dough is supple and silky smooth and small blisters develop just under its surface. Put the dough in a large well-greased bowl, turning the dough over so it's greased-side up. Cover the bowl with plastic wrap and refrigerate overnight.
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4
The next day, take the dough out of the refrigerator and punch it down. Transfer it from the bowl to your countertop and cover it with a kitchen towel. Let it rise a second time, at room temperature, for up to 90 minutes, or until almost doubled in size.
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5
While the dough rises, make the filling: In a small saucepan, combine the cherries, rum, and 1/4 cup water. Bring the mixture to a simmer, cook it for 2 minutes, then remove it from the heat and let it cool. Drain the liquid from the mixture and set the cherries aside in a small bowl.
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6
In a food processor, pulse the egg whites until they're foamy. Crumble in the pistachio paste and pulse again until it's thoroughly combined and smooth. Add the sugar and butter and pulse again to incorporate. Using a rubber spatula, scoop the mixture into a medium bowl. Add the lemon zest and stir to combine.
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7
Assemble the Danish: Preheat the oven to 350u00b0F. Line a baking sheet with parchment paper. In a 10-inch cast-iron skillet, melt1 teaspoon butter over low heat. Brush the melted butter over the bottom and sides of the pan to coat.
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8
Turn the dough out onto a lightly floured work surface. Cut it into 4 equal pieces; you will be making 2 twists. Roll each piece out to a 5 by 12-inch rectangle. Using a rubber spatula or the back of a spoon, spread one quarter of the pistachio paste mixture on each rectangle; dot each with one-quarter of the drained cherries. Roll each piece up from the long side, jelly-roll style. Pinch the edges and ends well to seal the seams and help keep the filling inside the dough. Place 2 of the filled rolls side-by-side, seams down. Twist one roll over the other, as tautly as possible, forming a thick rope. Pinch the ends of the twist to fuse the rolls together, and tuck or twist any less-than-pretty areas under, out of view. Repeat with the remaining rolls.
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9
Coil the first twisted rope into a small, tight, snaillike spiral circle and place it in the center of the skillet. Wrap the second twisted rope around it, tucking the edges under the inner coil to connect the two ropes.
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10
Beat the egg yolk with 2 tablespoons water to make an egg wash and brush the dough with it. Sprinkle the pistachios over the top, followed by the sugar and the salt. Cover the pan and let the dough rise once more until doubled in size, about 40 minutes.
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11
Bake the Danish until it's browned and cooked through, 30 to 35 minutes, rotating the pan 180 degrees halfway through. Remove it from the oven, leaving it in the skillet for a couple of minutes to set before transferring it to a wire rack to cool for about 30 minutes. You should be able to lift it out of the pan quite easily with a spatula. This is best eaten the same day it's baked. I don't even let mine cool; it's a bit messier, but I can't help myself.
