Warm milk in a small bowl in the microwave for about 30-45 seconds. Add 2 ¼ tsp active dry yeast and 1 tbsp sugar to milk and gently whisk. Allow yeast to activate/bloom for 10 minutes, until puffy and bubbly.
Using the dough hook attachment, combine all-purpose flour, eggs, salt, sugar, and yeast mixture in a stand mixture. Begin on low speed and gradually increase to medium speed as dough begins to form, about 5-8 minutes. If dough is too sticky (it sticks to your hand), add 1-2 tablespoons of flour and continue to knead.
Once dough has formed and is soft and smooth, add butter, one tablespoon at a time, allowing each tablespoon to become fully incorporated into the dough before adding the next. (dough may temporarily break apart but will come back together when you continue to knead in the mixer) Continue to knead dough for another 5 minutes.
Lightly oil a large bowl and add dough. Cover with a towel or plastic wrap and allow dough to rise until it has doubled in size, about 1-2 hours.
While dough is rising, let's make the filling. Follow the recipe for prune butter here: https://californiaprunes.org/recipe/prune-butter/ - Once prune butter is made, set aside and allow it to cool.
Once dough has doubled in size, turn dough out onto a well floured surface. Cut dough into four equally sized pieces and roll each piece into a ball and set aside. Grab one of the dough balls and roll into a large circle. Place a salad plate on top of the dough and trace a circle, cutting off any extra pieces. Add prune butter to the circle and set aside. Repeat this two more times, placing each layer on top of the other. For the top layer, simply roll the last piece of dough into a circle, tracing it with the salad plate and lay it on top without adding the prune butter.
Add dough to a parchment lined baking sheet. Place a small cup in the middle of the dough and cut the dough into 4 pieces, then 8, and then 16. (See video) Grab two pieces of dough and twist inward three times and pinch the ends together. Repeat for the remaining pieces.
Preheat oven to 350 degrees.
Cover dough with a towel and allow to rise again for 20-30 minutes, until it becomes slightly puffy.
Brush with a beaten egg. Bake for 20-25 minutes, until golden brown.