About an hour before you begin making this, place the milk and butter on the counter to bring them to room temperature.
Stir the yeast into the room temperature milk with a pinch of the sugar and let it rest for about 10 minutes until it has dissolved and started to froth.
While the yeast blooms, place all the remaining dough ingredients into a stand mixer bowl (except the butter, and the egg wash ingredients). Once the yeast and milk mixture is frothy, add it to the ingredients.
Using the dough hook attachment, knead everything together in the stand mixer on low speed for about 2 minutes or until it has come together into a ball.
Be sure your butter has softened to room temperature. After an initial 2-minute slow knead in the mixer, increase your speed to medium. Add the butter, one tablespoonful at a time.
After all the butter is incorporated, knead on medium speed for another 8 minutes or so, until the dough is smooth and glossy.
Cover the bowl with a towel and allow the dough to rise for about 1 ½ hour in a warm kitchen.
Make the cranberry 'jam'. Place the cranberries, sugar, orange juice and water in a small saucepan and bring to a boil. Turn down the heat and let it all simmer for about 10 minutes.
After an overnight rise, remove your dough from the fridge and turn it onto a floured board. Cut it into 4 equal pieces and shape them roughly into balls.
Slide the parchment paper and brioche carefully onto a baking sheet. Place the whole thing in the fridge for about 15 to 20 minutes to make it easier to slice cleanly.
Using a 3 to 4-inch round cookie-cutter, make a delicate imprint right in the center of your jam sandwich. Using a sharp chopping knife, slice 16 even cuts all around the outer edge of the center circle.
Pick-up 2 strips at a time and twist them outwards from each other twice. Press the edges together and repeat until you have a lovely star.
Cover with a clean towel and put the brioche in a warm place to rise for about 1 ½ hour.
Before putting the brioche in a 350F preheated oven, whisk the egg and 1 tsp milk together. Brush the brioche with a light layer of this egg wash to give it shine and color.
Bake the brioche for about 30 minutes or until the top is golden. Serve warm.
