Make the Pull-Apart Sweet Dough:
In the bowl of a stand mixer, combine 2 cups flour, sugar, yeast, and salt.
In a small saucepan, heat the milk and butter over low heat until the butter is melted. Remove from heat, add water, and let cool until the mixture reaches 120-130°F (about 1 minute). Stir in the vanilla extract.
Pour the milk mixture over the flour-yeast mixture and mix with a rubber spatula until moistened. Attach the bowl to the mixer fitted with a paddle attachment. On low speed, add the eggs, one at a time, mixing until combined. Add 1/2 cup flour and mix until the dough is smooth (about 30-45 seconds). Add 2 more tablespoons of flour and mix on medium speed until the dough is smooth, soft, and slightly sticky (about 45 seconds).
Turn the dough onto a lightly floured surface and knead gently until smooth and no longer sticky, about 1 minute, adding additional flour only if needed. Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place until doubled in size (45-60 minutes).
Make the Lemon Filling:
While the dough is rising, combine the sugar, lemon zest, and orange zest in a small bowl. Set aside.
Assemble the Coffee Cake:
Preheat the oven to 350°F. Lightly butter a 9×5-inch loaf pan.
Gently deflate the dough and roll it out on a lightly floured surface into a 20×12-inch rectangle.
Using a pastry brush, spread the melted butter evenly over the dough. Cut the dough crosswise into 5 strips, each 12×4 inches.
Sprinkle 1 1/2 tablespoons of the zest-sugar mixture on one strip and stack another strip on top. Repeat with the remaining strips, ending with a stack of 5 layers.
Cut the stack crosswise into 6 equal strips (about 4×2 inches each). Fit the layered strips into the prepared loaf pan, cut sides up, and let rise in a warm place for 30-50 minutes until puffy.
Bake for 30-35 minutes until the top is golden brown. Let cool in the pan for 10-15 minutes before removing from the pan.
Make the Cream Cheese Icing:
In a medium bowl, mix the cream cheese and confectioners’ sugar until smooth. Beat in the milk and lemon juice until creamy.
Brush the icing over the warm cake and let it drip down the sides.
Serve:
Serve by pulling apart the layers or slicing the cake into 1-inch slices. Enjoy!