Warm 1/2 cup of milk in the microwave for 30 seconds. Add it to the bread machine.
Add all of the other babka bread dough ingredients to the bread machine in the order listed.
Run the bread machine on the dough cycle. My machine takes 90 minutes to complete a dough cycle.
While the bread machine is making the dough, make the simple sugar syrup. Mix the sugar and water in a small saucepan. Bring the mixture to a low boil, stirring to dissolve the sugar. Set aside to cool.
Make the cinnamon filling by combining all ingredients listed. Mix the ingredients in a medium bowl until you have a smooth spread that's about the consistency of peanut butter. If your butter has not softened enough, you can put the mixture in the microwave for a very brief time, 5-10 seconds.
In a small mixing bowl, make the streusel topping by mixing all streusel ingredients together using a pastry blender or fork.
Prepare the cake pan and bread pan by greasing or lining the pans with foil.
When the dough cycle has completed, remove the dough from the bread machine pan and divide it into three equal pieces. You will use two of the sections to make the cinnamon babka cake, and the other section to make a babka loaf.
Roll out each of the two sections of dough into a rectangle, approximately 18 inches by 12 inches. Spread the cinnamon filling evenly over each rectangle. Starting at the top, roll the dough down to encase the filling inside. Trim 1/2 inch off of each end so that the ends are even. (I like to place the rolled up scraps into a muffin tin and bake separately for about 15 minutes to have as a little snack.) Set aside while you roll out and fill the other dough section.
When both rolls are complete and trimmed, slice each roll in half lengthwise. Lay each half so that the filled layers are facing up to make a number (#) sign. Use the basket-weaving technique to weave the filled roll halves together. If you haven’t watched the video yet, now would be a good time. The video shows the technique, and you can pause it as often as you need.
Gently gather the woven dough and place it in the bread pan. If you are making a separate loaf with the other section of dough, place it in the bread pan. Cover and let rise for 30 minutes.
While the loaves are rising, turn the oven on to 350 degrees. Bake the cinnamon babka cake and the loaf for 20 minutes, then remove from oven and brush the cake and loaf with two coats of simple syrup. Sprinkle the streusel topping on top of the cinamon babka cake and return the loaf and cake to the oven.
Bake for another 15 minutes. When the cake and loaf are removed from the oven, brush the loaf immediately with another 3 light layers of syrup, but leave the cinnamon babka cake alone so as not to disturb the lovely streusel topping. Allow the cake and loaf to cool for 5 minutes, then gently go around the edge of each pan with a spatula or butter knife. Gently remove the cake and loaf from the pan and set on a wire rack to cool further.