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1
In a medium bowl, add the yeast, 1 teaspoon sugar, and warm water. Let the yeast rest until it proofs (5 minutes).
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2
Once the yeast has proofed, add the egg, milk, sugar, and salt. Stir with a whisk, and set to the side.
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3
Place the flour and cubed butter into a large bowl. With a pastry blender, combine until the butter is in tiny pieces. (You can also use the food processor for this step.)
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4
Add the wet ingredients to the flour and combine until the dough comes together. Place the dough onto a floured work surface and shape into a square. Roll the dough into a rectangle 9 x 13-inches. Fold the dough lengthwise into thirds (similar to folding a letter to fit into an envelope). Roll the dough into a rectangle again, and then again fold into thirds. Repeat this process twice more, until you've done it a total of 3 times. Cut the dough in half, wrap each piece in plastic wrap, and place in the fridge overnight. The dough keeps for one week in the fridge and 2 months in the freezer.
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5
In a large pot on low, heat 2 tablepsoons of butter until it begins to foam. In a small bowl combine the sugar, flour, and cinnamon. Add the sliced apples and the cinnamon sugar mixture to the pot and toss. Cook until all the liquid has evaporated and the apples are tender, about 15 minutes. Remove from the heat and let cool for 30 minutes.
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6
Preheat the oven to 400u00b0 F.
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7
Remove one piece of dough from the fridge, and save the other for a rainy day (the dough can last in the fridge for up to 5 days and in the freezer for 3 months). On a floured piece of parchment paper, roll out the dough into a 9 x 13-inch rectangle. Place the apples down in the middle of the dough. With the dough laid in front of you vertically (so that the smaller 9-inch end is facing you), make 1-inch diagonal cuts down the left and right sides of the dough (imagine you are making a Christmas tree). Once you have reached the bottom, cut away two triangle pieces, so that the dough now has a tree trunk. Fold the tree trunk flap over the apples, then go back to the top and fold each strip over the apples, alternating from left to right and moving towards the bottom.
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8
Gently lift the parchment paper and the braid onto a baking sheet. Brush the top of the pastry with an egg wash (one egg white and a teaspoon of water). Bake for 15 to 20 minutes, or until brown on top.
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9
In a small bowl, whisk the powdered sugar, 1 tablespoon of milk, and vanilla until you get a desired consistency. Add a tablespoon more milk if the icing is too thick. (It should be pourable, but not so thin that it drips off of the pastry.) Drizzle over the top of the braid and sprinkle with powdered sugar. Serve warm. The danish lasts for 3 to 4 days. It's best to store in the fridge, covered in plastic wrap, and then reheated in the oven or microwave before eating.
