Step 1: Make the Dough

1. In a small bowl, combine warm milk, warm water, and sugar. Stir in the yeast and let it sit for 5-10 minutes until bubbly and frothy.
2. In a large mixing bowl, whisk together flour and salt. Add the yeast mixture, melted butter, and egg. Mix until a dough forms.
3. Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Place it in a lightly greased bowl, cover, and let rise for 1-1.5 hours, or until doubled in size.

Step 2: Prepare the Blackberry Filling

1. In a saucepan, combine the blackberries, sugar, cornstarch, and vanilla extract. Cook over medium heat, stirring occasionally, until the mixture thickens and the berries soften, about 5-7 minutes.
2. Remove from heat and let cool slightly.

Step 3: Roll Out the Dough

1. Once the dough has risen, punch it down and roll it out on a floured surface into a 12×18-inch rectangle.
2. Spread the softened butter over the dough, then evenly spread the cooled blackberry mixture over the surface.

Step 4: Roll and Slice

1. Starting from the long edge, carefully roll the dough into a log. Slice into 12 equal pieces.
2. Place the rolls into a greased 9×13-inch baking dish, making sure they are snug but not too tight.

Step 5: Let the Rolls Rise

1. Cover the baking dish with a clean kitchen towel and let the rolls rise for another 30-45 minutes until puffed up.

Step 6: Bake the Rolls

1. Preheat your oven to 350°F (175°C).
2. Bake the rolls for 25-30 minutes, or until golden brown on top.

Step 7: Make the Cream Cheese Frosting

1. In a bowl, beat together the cream cheese and butter until smooth.
2. Gradually add the powdered sugar and vanilla extract, and mix until creamy. Add milk a little at a time until you reach your desired consistency.

Step 8: Frost & Serve

1. Once the rolls are baked, remove them from the oven and let cool slightly.
2. Spread the cream cheese frosting generously over the warm rolls, letting it melt into the soft dough.