Special equipment: An instant-read thermometer
Bring the milk just to a boil over medium heat in a small pot. Remove from the heat and add the butter to melt. Transfer the mixture to a bowl and let cool to between 105 to 110 degrees F. Add the egg and stir to combine.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, yeast, salt and 3 tablespoons of the granulated sugar. Add the milk mixture and mix until just combined. Switch to the dough hook and knead the dough on low speed until it is smooth and elastic, about 6 minutes. (You could also do all of this by hand.) Form the dough into a ball and transfer it to a buttered bowl. Cover with plastic wrap and set aside to double, about 1 hour. Butter a 12-cup nonstick muffin tin (the cups and the top) really well.
On a very lightly floured surface, roll the dough out to about a 12-by-15-inch rectangle. Toss the blueberries with the cornstarch. Sprinkle the dough with the remaining 1/4 cup granulated sugar, then sprinkle with the blueberry mixture. Roll the dough up into a tight coil, then cut into 12 equal pieces. Set a piece of dough cut-side up into each cup in the muffin tin. Cover with plastic wrap and transfer to the fridge overnight.
About 3 hours before you want to eat, take the buns out of the refrigerator. Let stand until doubled in size, 2 to 2 1/2 hours.
Preheat the oven to 350 degrees F.
Bake the buns until golden brown and set, 20 to 24 minutes. Transfer the muffin tin to a rack to cool for about 10 minutes, then use a small offset spatula to loosen and lift the buns out of the tin. Serve warm sprinkled with confectioners' sugar.
If you don't have nonstick muffin tins, bake these buns in a 9-inch square baking pan or a 9-inch cake pan. Just cut the dough into 9 pieces instead of 12. They will be slightly larger.