Step 1: In a large mixing bowl, whisk together the warm milk, sugar, and yeast. Let it stand for 5-10 minutes until it becomes foamy.
Step 2: Stir in the softened butter, salt, and half of the flour. Gradually add the remaining flour while kneading by hand or with a stand mixer until a smooth, slightly tacky dough forms.
Step 3: Cover the bowl with a clean cloth and let the dough rise in a warm, draft-free area for about 60-90 minutes until it has doubled in size.
Step 4: In a medium bowl, combine the shredded chicken, mayonnaise, Sriracha, minced garlic, and sliced green onions. Mix well until the chicken is evenly coated.
Step 5: Preheat your oven to 375°F (190°C) and line a large baking sheet with parchment paper.
Step 6: Punch down the risen dough and turn it out onto a lightly floured surface. Divide the dough into 12 equal portions.
Step 7: Flatten each portion into a circle. Place about 2 tablespoons of the chicken mixture and a generous amount of mozzarella cheese in the center.
Step 8: Bring the edges of the dough together and pinch firmly to seal the filling inside. Shape into a smooth ball.
Step 9: Place the buns on the prepared baking sheet, seam-side down. Brush the tops with an egg wash or melted butter if desired.
Step 10: Bake for 20-25 minutes, or until the buns are a beautiful golden brown color. Serve warm.