1. Make the dough (first 9 ingredients). Combine dry ingredients: flour, yeast, sugar and salt. In a small saucepan, heat butter and milk over low heat just until the butter is melted. Add water and vanilla extract.
2. Combine 1/2 of the dry ingredients and milk mixture. Mix well with a spatula. Using an electric mixer (on low speed), add eggs, 1 at a time, mixing just until incorporated. Gradually add the rest of the flour mixture, mixing with a spoon, then your hands. Knead the dough until smooth and soft, but not sticky (if it is, add another tablespoon of flour).
3. Cover with plastic wrap and let rise in a warm place for 1 hour.
4. Meanwhile, prepare the filling. In a bowl, mix melted butter, sugar, lemon zest and orange zest.
5. On a lightly floured surface, roll out the dough into a 20-by-12-inch rectangle. Using a pizza cutter, cut the dough into 5 even strips (12-by-4-inch each).
6. Spread 1/5 of the filling over one of the rectangles. Top with the second rectangle and spread some filling over it. Repeat with the remaining dough and filling, so that you get a stack of 5 rectangles.
7. Slice the dough stack crosswise through all 5 layers in order to get 6 equal strips (about 4-by-2-inch each).
8. Brush 9-by-5-inch loaf pan with oil. Arrange these layered strips into the prepared loaf pan, side by side, cut edges up.
9. Cover with plastic wrap and let rise in a warm place for about 30 minutes (if you don't have the time, skip this step).
10. Preheat oven to 350 degrees F (180 degrees C).
11. Bake in the preheated oven for 30-40 minutes, until the top is golden brown and a toothpick inserted in the center of the cake, comes out clean.
12. While the cake is baking, prepare the glaze. In a bowl, using a rubber spatula, mix cream cheese and powdered sugar until smooth. Add milk and lemon juice and mix until smooth.
13. Cool the cake in a pan for 10-15 minutes, then remove from the pan.
13. Using a pastry brush, brush the top of the cake with cream cheese icing.
14. To serve you can pull it apart or slice. Enjoy!