Preheat your oven to 375°F (190°C) and grease a 9-inch round baking dish.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, and salt.
In another bowl, mix the softened butter, milk, egg, and vanilla extract until well combined.
Gradually add the wet ingredients to the dry ingredients, stirring until a dough forms.
On a floured surface, roll out the dough into a rectangle about 1/4 inch thick.
Spread the softened butter over the dough, then sprinkle the brown sugar and cinnamon evenly on top.
Scatter the blueberries over the cinnamon mixture.
Starting from one long side, carefully roll the dough into a tight log.
Slice the log into 12 equal pieces and place them in the prepared baking dish.
Bake for 20-25 minutes or until golden brown.
While the rolls are baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the rolls are out of the oven, let them cool for 5 minutes before drizzling the glaze over the top.