Prepare the Dough: In a large mixing bowl, combine the flour, sugar, salt, and instant yeast. Gradually warm the milk and water, then pour over dry ingredients with softened butter. Mix until a shaggy dough forms and knead for 8-10 minutes.

Let the Dough Rise: Place kneaded dough in a greased bowl, cover, and let rise in a warm area for about 1 hour.

Sauté the Filling: In a skillet, heat olive oil, add onion, and sauté until translucent. Add garlic and cook until fragrant. Stir in tomato paste, smoked paprika, cumin, and hot sauce.

Mix in the Chicken and Cheese: Add shredded chicken, then remove from heat. Mix in softened cream cheese and mozzarella until creamy.

Shape the Buns: After rising, punch down the dough and divide into 12 portions. Flatten each piece and fill with the chicken mixture. Fold edges over and seal.

Let the Buns Rest: Arrange filled buns on a parchment-lined sheet, cover loosely, and let rest for 10-15 minutes.

Bake the Buns: Preheat oven to 375°F. Brush buns with a beaten egg and bake for 18-20 minutes.

Cool and Serve: Let buns cool slightly on a wire rack, garnish if desired, and serve warm.