Heat the milk and butter in the microwave until butter is melted and mixture is warm to the touch, but not hot. This took me about 45 seconds.
Stir the yeast and sugar into the milk and butter mixture and set aside for 5 minutes.
In a small bowl stir together the cinnamon, ginger, nutmeg and cloves. Set aside.
Add flour, salt and half of your spice mixture to the bowl of a stand mixer, and mix with a fork or your hand to combine.
Take a look at your yeast mixture – it should be frothy and starting to bubble. Add it to the dry ingredients along with the egg yolk, pumpkin puree, and vanilla.
Using a dough hook attachment, mix for 7-8 minutes. The dough should pull away from the edges of the bowl and stick to the bottom. It will still be sticky to the touch, but shouldn’t be an enormous mess – if it is add some of the remaining flour. I found that I needed about ¼ C extra flour before all was said and done.
Place the dough in a greased bowl and cover with plastic wrap. Let it rise in a warm spot for about an hour, or until it has doubled in size.
After the hour, transfer the dough to a well-floured surface and roll into a rectangle 12 by 18 inches.
In a small bowl mix together the softened butter, salt, dark brown sugar, pumpkin puree, and the remaining spice mixture. Spread this mixture all over the dough in an even layer, leaving a ½ inch space on one of the long sides.
Starting at the long end without the ½ inch space, roll the dough into a tight log. I find this is easiest by working in small increments from left to right and then back the other direction. When you’ve reached the end pull the remaining dough up and over the top of your roll and pinch to seal all the way across to form a seam.
Trim the ends and slice the whole roll down the middle, vertically. Move the two pieces so that the filling is exposed and facing up. Then carefully move one piece under and over the other and repeat until you have a braided twist. Bring the ends of the braid to meet and pinch together to form a ring. Transfer the babka ring to a 9 inch cake pan (I used a spring-form), cover with plastic wrap and let rise for 45 minutes.
While the babka ring rises, preheats your oven to 375° F.
Remove the plastic wrap and bake your babka for 45-55 minutes, or until it reaches an internal temperature of 195° F. If you bake yours in a spring-form pan like I did, make sure to place it on top of a rimmed baking sheet, in case it leaks – lest you want to spend an eternity scrubbing the floor of your oven.
Let the babka cool in the pan for 15 minutes. Then remove from the pan and finish cooling on a rack.
If you’re making the cream cheese icing (which I highly recommend) whisk together all the ingredients in a small bowl and get ready to drizzle.
Drizzle with icing, or if not using dust with powdered sugar, slice and serve.
