In a large bowl, whisk warm milk, yeast, and granulated sugar. Let stand 5–10 minutes until foamy.
Whisk in the egg and melted butter. Add flour and salt; mix until a soft dough forms.
Knead on a lightly floured surface for 6–8 minutes (or use a stand mixer with a dough hook) until smooth and slightly tacky.
Place dough in a greased bowl, cover, and let rise in a warm spot until doubled, 60–90 minutes.
For the filling, stir together brown sugar, cinnamon, and flour. Roll dough into a 14×9-inch rectangle. Spread softened butter over the surface.
Sprinkle cinnamon-sugar mixture evenly over the buttered dough, then distribute blueberries evenly.
Starting from the long side, roll the dough into a tight log and pinch the seam to seal. Cut into 9–12 rolls using unflavored dental floss or a sharp knife.
Arrange rolls in a greased 9×13-inch baking dish. Cover and let rise until puffy, 30–45 minutes. Meanwhile, preheat oven to 350°F (175°C).
Bake 22–25 minutes, or until golden and the centers register about 190°F.
For the frosting, beat cream cheese and softened butter until smooth. Add powdered sugar, blueberry jam (or compote), vanilla, and a pinch of salt; mix until creamy.
Cool rolls for 10–15 minutes, then spread frosting over warm rolls. Serve and enjoy.