Braided Coffee Cake with Apple-Ginger Filling

For the dough:Coat a large bowl with butter and set aside.

Place the milk and water in a small heatproof bowl or measuring cup and warm in the microwave until the mixture reaches 100°F to 115°F (this can also be done in a small saucepan on the stovetop over low heat).

Transfer the mixture to the bowl of a stand mixer and sprinkle the yeast on top. Set aside until foamy, about 5 to 10 minutes.

Add the eggs, sugar, and salt to the yeast mixture and whisk until evenly combined.

Add the flour and attach the bowl to a stand mixer fitted with a dough hook.

Mix on low speed until the flour is incorporated and the dough just comes together, about 1 minute.Increase the speed to medium high and add the measured butter 1 piece at a time, letting each piece completely incorporate before adding the next. Continue mixing until the butter is completely incorporated and the dough is smooth and pulling away from the sides of the bowl (the dough will be soft and slightly sticky), about 10 minutes total.

Transfer the dough to the prepared bowl and turn it to coat with the butter. Cover the bowl tightly with plastic wrap, place it in the refrigerator, and let the dough rise overnight or up to 18 hours. Meanwhile, make the filling. (If you’re baking the cake the same day, cover the bowl tightly with plastic wrap and leave it in a warm place until the dough doubles in size, about 90 minutes. Punch the dough down, cover again with plastic wrap, return to the warm place, and let rise again until doubled, about 45 to 60 minutes more.)For the filling:Peel, core, and cut the apples into small dice.

Heat the butter in a large frying pan over medium heat until foaming.

Add the apples, sugar, cinnamon, and salt and cook, stirring occasionally, until the sugar dissolves and the mixture starts to bubble, about 5 minutes. Reduce the heat to medium low and simmer, stirring occasionally, until the apples are cooked through but still firm, about 5 minutes more. Meanwhile, set a fine-mesh strainer over a medium heatproof bowl.

Remove the pan from the heat.

Pour the apple mixture into the strainer and gently stir until only apple pieces remain.

Transfer the apple pieces to a medium bowl and stir in the ginger; save the liquid for another use.

Cut an 11-by-14-inch piece of parchment paper and place it near your work surface.Lightly flour the work surface and a rolling pin.

Place the dough on the work surface and roll it into an 8-by-12-inch rectangle. Drape it over the rolling pin, transfer it to the parchment paper, and position it with one of the shorter ends of the rectangle nearest you. If needed, gently stretch the dough back into a rectangle.Evenly spread the apple filling lengthwise down the center of the dough, leaving about a 1/2-inch border on the top and bottom and about a 3-inch border on each side. Using a pastry brush, lightly brush a 1-inch border on the left and right edges of the dough with 2 teaspoons of the milk (you will not use it all; reserve the rest for later). Using kitchen scissors, a pizza cutter, or a sharp paring knife, make 7 horizontal 2-inch cuts through the dough on the left and right sides of the filling about 1 1/2 inches apart (you should have 8 flaps on each side). Fold the top left flap over the apple filling, making sure to pull the flap completely over the filling. Fold the top right flap over to completely cover the left flap. Pinch the bottom seams together where the flaps touch, and tuck the bottom left corner of the right flap underneath. Working your way from top to bottom, repeat with the remaining flaps, leaving about a 1/2-inch gap of exposed filling between each folded row. For the bottom flaps, fold the left flap over the filling, fold the right flap over the left, and tuck the top left corner underneath.

Transfer the braided dough along with the parchment paper to a baking sheet. Cover completely with plastic wrap and let rise in a warm place until puffed and almost doubled, about 2 hours. (If the dough was made the same day, it will only take about 30 minutes to rise.)

Heat the oven to 350°F and arrange a rack in the middle.

Brush the top of the braided dough with what’s left of the 2 teaspoons of milk.

Bake the coffee cake until it’s golden brown and puffed and an instant-read thermometer inserted in the center reads 190°F, about 20 minutes.

Transfer the cake and parchment paper to a wire rack and let cool for 20 minutes. Meanwhile, make the glaze.

Whisk the powdered sugar, remaining 2 tablespoons of milk, and vanilla in a medium bowl until smooth and viscous; set aside. (If the glaze is too thick, whisk in additional milk, 1 teaspoon at a time, until it reaches the desired consistency.) Set aside.Using a fork or whisk, drizzle the glaze over the cake, moving quickly back and forth over the top.

Let the cake cool at least 10 minutes more. To serve, slide a large, flat spatula under the cake, transfer it to a cutting board or serving platter, and use a serrated knife to slice.