Make the Dough: In a small saucepan, warm the milk and water over medium-low heat until it reaches 105–115°F—warm to the touch but not hot. Pour into your stand mixer bowl, sprinkle in the yeast and 2 teaspoons of sugar, and stir. Let it sit for 5–10 minutes, until foamy.
Add the remaining sugar, melted butter, egg, egg yolk, salt, and 2 cups of flour. Mix on low speed with a dough hook until combined. Continue adding flour, ½ cup at a time, until the dough pulls away from the sides of the bowl and feels soft but not sticky.
Knead for 5–10 minutes, either by hand or in the mixer, until the dough is smooth and stretchy. Place it in a lightly oiled bowl, cover with plastic wrap, and set it in a warm place to rise until doubled in size (about 1–2 hours).
Prepare the Filling: In a small bowl, stir together brown sugar, cinnamon, and a pinch of salt. Make sure your butter is soft enough to spread easily—it shouldn’t be melted.
Assemble the Star Bread: Once the dough has risen, divide it into two equal halves—each will make one star. Cut each half into four equal pieces. On a lightly floured surface, roll each piece into a 10-inch circle.
Place one circle on a parchment-lined baking sheet. Spread with a thin layer of butter and sprinkle the cinnamon-sugar mixture evenly on top. Repeat with the next two layers, ending with a plain dough circle on top. Trim the edges to form a neat, even circle.
Use a small glass or cookie cutter to mark the center, then cut 16 equal strips radiating outward. Twist two strips away from each other twice and pinch the ends together to form a point. Continue all the way around to create the star shape.
Bake: Preheat the oven to 350°F. Whisk 1 egg with a splash of water for an egg wash and brush it over the top. Sprinkle with coarse sugar if desired.
Bake for 17–20 minutes, until golden brown and the inside reaches 190°F. If the top darkens too quickly, lower the oven temperature slightly. Let the bread cool before serving.
Store leftovers in an airtight container for up to 3 days, or freeze to enjoy later.