Make the Dough:
In a mixing bowl, combine warm milk, sugar, and yeast. Let sit for 5-10 minutes until foamy. Add melted butter, egg, and salt. Gradually mix in flour until a soft dough forms. Knead for 5-7 minutes by hand or use a stand mixer with a dough hook. Place the dough in a greased bowl, cover, and let it rise for 1 hour or until doubled in size.
Prepare the Filling:
In a small bowl, mix the softened butter, brown sugar, and cinnamon until well combined.
Roll and Fill the Dough:
Roll the dough out into a large rectangle (about 16x12 inches). Spread the cinnamon-sugar mixture evenly over the dough, leaving a small border. Sprinkle the blueberries evenly across the top.
Roll and Cut:
Starting from the long edge, tightly roll up the dough into a log. Slice into 12 equal pieces and place them into a greased 9x13-inch baking dish.
Let Them Rise:
Cover the dish with a towel and let the rolls rise for another 30 minutes until they puff up.
Bake:
Preheat the oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until golden brown.
Make the Cream Cheese Glaze:
In a small saucepan or mixing bowl, whisk together the cream cheese, powdered sugar, milk, and vanilla until smooth and pourable.
Glaze and Serve:
Once the rolls are out of the oven, let them cool slightly. Drizzle the cream cheese glaze generously over the warm rolls.