Mix warm milk, sugar, and yeast in a bowl and let sit for about 10 minutes until foamy.
Add eggs, softened butter, flour, and salt to the yeast mixture. Knead until smooth and elastic. Cover and let rise in a warm place for about one hour until doubled in size.
Melt butter in a pan over medium heat. Add minced garlic and cook for about two minutes until fragrant. Stir in chopped herbs and set aside.
Once risen, roll out the dough into a large rectangle on a floured surface. Brush generously with the garlic herb butter mixture and sprinkle shredded mozzarella evenly over the top.
Roll the dough tightly into a log from one long side to another. Slice it lengthwise down the middle to expose the swirls inside. Twist both halves together with cut sides facing up.
Place your twisted dough into a greased baking pan. Cover it again and let rise for another 30–40 minutes until puffed up nicely.
Preheat your oven to 350°F (175°C). Brush the top with an egg wash made by combining one egg with water. Bake for about 35–40 minutes until golden brown on top.
Let cool in the pan for about 15 minutes before slicing. Serve warm.