In a large mixing bowl, combine flour, sugar, salt, and instant yeast. Warm milk and water until body temperature, then add to dry ingredients with softened butter. Knead for 8–10 minutes until smooth, cover, and let rise for 1 hour.

Heat olive oil in a skillet over medium heat. Sauté chopped onions for 5 minutes, add minced garlic and stir for 30 seconds. Incorporate tomato paste, smoked paprika, cumin, and hot sauce, then stir in shredded chicken and heat through. Mix in cream cheese and mozzarella until creamy.

Once the dough has risen, punch it down and divide into equal portions. Flatten each piece, place filling in the center, fold edges over, and shape into a ball. Arrange on a baking tray and let rest for 10–15 minutes.

Preheat your oven to 375°F (190°C). Brush the tops of the buns with a beaten egg. Bake for 18–20 minutes until golden brown and puffy. Cool slightly on a wire rack before serving.