Combine 2 cups (280 g) flour, yeast, sugar, and salt in a large mixer bowl; mix on low speed until incorporated. Heat milk in a microwave-safe measuring cup for 45 seconds to 1 minute, until very warm (120-130°F). Add warm milk, butter, and egg to flour mixture and mix until combined; mix in remaining flour. Switch out the flat beater for a dough hook, and knead dough for 5 minutes until smooth and elastic. The dough is ready when it feels tacky but doesn't stick to your fingers (if necessary, add additional flour 1 tablespoon at a time while kneading).
Place dough in a large bowl coated with nonstick spray and cover with plastic. Let the dough rise in a warm place until doubled in size, about 40 minutes. To check if dough has doubled, lightly flour two fingers and press them down into center of dough. If indentations remain, gently press down dough; cover and let rest 5 minutes. Spray a 13 x 9-inch baking dish (or two 9-inch round pans) with nonstick spray.
Turn dough out on a lightly floured board and roll into an 18 x 12-inch rectangle. Brush dough with melted butter, leaving a 1/4-inch border. Sprinkle brown sugar and cinnamon over dough; top with blueberries, pressing gently into dough. Carefully roll dough up into a tight log and pinch edges to seal.
Trim off uneven ends and score dough into 18 equal slices. Use unflavored dental floss to slice dough crosswise (slip a long slice of floss under log of dough and cross on top to cut slices cleanly). Place rolls cut side up into prepared baking dish. Cover loosely with plastic and let rise in a warm place until doubled in size, about 30 minutes.
While the rolls rise, preheat oven to 350°F. Bake rolls for about 18 minutes, until lightly golden. Remove from oven to cool on a wire rack for 5 minutes. To prepare glaze, whisk together powdered sugar, butter, milk, and vanilla in a small bowl. Pour glaze over warm rolls; glaze will set as rolls cool.