Make the pull-apart sweet dough

Cup of Yum
1. In the bowl of a stand mixer, stir together 2 cups (9 ounces) of the flour, the sugar, yeast, and salt.
2. In a small saucepan, heat the milk and butter over low heat just until the butter is melted. Remove from the heat, add the water, and set aside until warm (120 to 130°F [49 to 54°C]), about 1 minute. Add the vanilla extract.
3. Pour the milk mixture over the flour-yeast mixture and, using a rubber spatula, mix until the dry ingredients are evenly moistened. Attach the bowl to the mixer, and fit the mixer with the paddle attachment. With the mixer on low speed, add the eggs, 1 at a time, mixing just until incorporated after each addition. Stop the mixer, add 1/2 cup (2 1/4 ounces) flour, and resume mixing on low speed until the dough is smooth, 30 to 45 seconds. Add 2 more tablespoons flour and mix on medium speed until the dough is smooth, soft, and slightly sticky, about 45 seconds.
4. Sprinkle a work surface with 1 tablespoon flour and turn the dough onto the flour. Knead gently until the dough is smooth and no longer sticky, about 1 minute, adding an additional 1 to 2 tablespoons flour only if the dough is unworkably sticky. Place the dough in a large bowl, cover the bowl tightly with plastic wrap, and let the dough rise in a warm place (about 70°F [21°C]) until doubled in size, 45 to 60 minutes. Press the dough gently with a fingertip. If the indentation remains, the dough is ready for the next step.

Make the lemon filling

1. While the dough is rising, in a small bowl, mix together the sugar, lemon zest, and orange zest. Set aside. (The sugar draws out moisture from the zests to create a sandy-wet consistency, so don't be alarmed when you see this.)

Assemble the coffee cake

1. Adjust the oven rack to the center position and preheat the oven to 350°F (175°C). Lightly butter a 9-by-5-by-3-inch loaf pan.
2. Gently deflate the dough. On a lightly floured work surface, roll the dough into a 20-by-12-inch rectangle with a short edge facing you. Using a pastry brush, spread the melted butter generously over the dough. Cut the dough crosswise into 5 strips, each about 12 by 4 inches. (A pizza cutter is helpful here.) Sprinkle 1 1/2 tablespoons of the zest-sugar mixture over 1 of these buttered strips. Top with a second strip and sprinkle it with 1 1/2 tablespoons of the zest-sugar mixture. Repeat with the remaining strips and zest-sugar mixture, ending with a stack of 5 rectangles. Work carefully when adding the crumbly zest filling, or it will fall off when you have to lift the stacked pastry later.
3. Slice the stack crosswise through the 5 layers to create 6 equal strips, each about 4 by 2 inches. Fit these layered strips into the prepared loaf pan, cut edges up and side by side. (While there is plenty of space on either side of the 6 strips widthwise in the pan, fitting the strips lengthwise is tight. But that's fine because the spaces between the dough and the sides of the pan fill in during baking.) Loosely cover the pan with plastic wrap and let the dough rise in a warm place (70 °F [21°C]) until puffy and almost doubled in size, 30 to 50 minutes. Press the dough gently with a fingertip. If the indentation remains, the dough is ready for baking.
4. Bake the coffee cake until the top is golden brown, 30 to 35 minutes. Place on a wire rack and let cool in the pan for 10 to 15 minutes.

Make the cream cheese icing

1. In a medium bowl with a rubber spatula, vigorously mix the cream cheese and sugar until smooth. Beat in the milk and lemon juice until the mixture is creamy and smooth.
2. Tilt and rotate the pan while gently tapping it on the counter to release the cake sides or simply slip a thin knife or spatula between the coffee cake and the pan. Invert a wire rack on top of the coffee cake, invert the cake onto the rack, and carefully lift off the pan. Invert another rack on top, invert the cake so it is right side up, and remove the original rack.
3. Slip a sheet of waxed paper under the rack to catch any drips from the icing. Using a pastry brush, coat the top of the warm cake with the icing to glaze it. (Cover and refrigerate the leftover icing for another use. It will keep for up to 2 days.)
4. To serve, you can pull apart the layers, or you can cut the cake into 1-inch-thick slices on a slight diagonal with a long, serrated knife. If you decide to cut the cake rather than pull it apart, don't attempt to cut it until it's almost completely cool.