Using a large glass measuring bowl, add the milk, water, and cubed butter. Heat it in the microwave or a saucepan until warm, but not boiling. The butter will melt, but there should be some solid pieces floating. The warm milk mixture needs to be warm enough to activate the yeast, but not so hot that it kills it. Aim for 110°F.
In a stand mixer, combine all of the dry ingredients EXCEPT one cup of flour. This will be added as needed. Mix the dry ingredients together and then pour in the warm liquid mixture. Attach the bowl and dough hook to the stand mixer and begin kneading on a low speed (slow and gentle). Form into ball shape with your hands
Continuing on a slow speed, add the remaining one cup of flour, a few tablespoons at a time until the dough clings to the hook and the sides of the bowl are clean. I usually have to add the entire cup of flour, for reference. Knead for two minutes more.
While the dough is kneading, bring a cup of water to a boil in the microwave and leave the door shut. This will create a warm and humid proofing box to help the dough be even fluffier.
Transfer the dough too a lightly greased large mixing bowl (or grease the mixing bowl it was made in) and cover the dough with a loose tea towel.
Quickly put the dough into the microwave and close the door. Let the dough rise for 45 minutes to an hour.
Turn dough onto a lightly floured surface or silicon pie mat. The pie mat makes it so much easier! It already has the circle size marked, so it's easy to shape the star bread. Divide the dough into 4 equal pieces. Set aside three of the dough balls and create the first layer by pressing the dough into a 12 inch circle. You can do this with your hands and don't need a rolling pin. Transfer this layer to a sheet of parchment paper on a pizza pan or baking sheet.
Spread warmed jam or jelly over the dough circle, leaving about an inch along the edges free of the sweet filling.
Take another ball of dough and create the second circle. Gently pick up the circle and place it over the bottom layer and jam. Press the edges lightly to seal.
Place a round prep bowl, biscuit cutter or other small circle in the center of the dough circle. Using a pizza cutter or sharp knife, divide the dough into four sections, then divide each section into 4 equal strips for a total of 16 segments.
Create a star shape by taking two adjacent strips of dough and twisting them twice away from each other while keeping the layers of dough together. Pinch the ends together to form the star points. See diagram above.
Cover with a tea towel, place dough in a warm spot and perform a second rise for 20-30 minutes until the top of the stars have domed nicely.
Preheat the oven to 350°. Use a pastry brush to lightly brush a thin coat of milk over each star bread. Sprinkle with sugar. Bake the bread for 50 to 60 minutes, until the crust is golden brown and the sides of the loaf feel firm. The internal temperature of the loaf should be about 195°F.
Remove the loaf from the oven and let it sit on the pan for 5-10 minutes. Leave the star on the parchment, and slide it on a cooling rack to cool. Let it cool completely before slicing. You can choose to leave the parchment underneath for stability or remove it, just make sure not to serve any pieces of parchment to your guests!
In a stand mixer with whisk attachment, add the cream cheese, butter, powdered sugar and vanilla. Whisk for several minutes until light and fluffy. Frost the stars while they are still warm from baking.