In a small saucepan, combine warm milk and water. Heat over medium-low, stirring occasionally, until the mixture reaches 105–115°F, ensuring even heating.
Pour the mixture into the bowl of a stand mixer. Sprinkle yeast and 2 tsp of sugar over it, stir, and let sit for 5–10 minutes until foamy.
Add the remaining sugar, melted butter, egg, egg yolk, salt, and 2 cups of flour to the yeast mixture. Mix on low speed using a dough hook until combined.
Gradually add more flour, ½ cup at a time, until a soft dough forms and pulls away from the bowl. The dough should feel slightly tacky but not sticky.
Knead for 5–10 minutes on low speed or by hand on a lightly floured work surface. Once smooth and elastic, transfer the dough to a lightly oiled bowl. Cover with plastic wrap and let the dough rise in a warm place until doubled (about 1–2 hours).
Preparing the Filling
In a small bowl, combine brown sugar, cinnamon, and salt.
Ensure the butter is softened enough to spread easily.
Assembling the Star Bread
Divide the dough into two equal halves—these will form your two stars. Next, cut each half into four equal pieces using a bench scraper or sharp knife. On a lightly floured work surface, roll each piece of dough into a 10-inch circle, creating the layers for your stars.
Place the first circle on a piece of parchment paper set on a prepared baking sheet. Spread a thin coat of butter over the top of the dough and sprinkle evenly with the cinnamon-sugar mixture.
Repeat with the second circle, third circle, and sweet filling, topping with the final circle of dough (leave it plain). Trim the edges to form an even circle using a pizza cutter or biscuit cutter.
Use a cookie cutter or glass to mark the center. Cut 16 equal strips radiating outward. Twist pairs of strips away from each other twice, then pinch the ends together to form star points.
Baking
Preheat your oven to 350°F. Lightly brush the top of the dough with an egg wash (1 egg whisked with water) and sprinkle with coarse sugar if desired.
Bake for 17–20 minutes or until golden brown and the internal temperature reaches 190°F. If the top browns too quickly, turn oven down slightly.
Allow the bread to cool before serving. Store any leftover star bread in an airtight container for up to 3 days, or freeze for the next day.