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Heat the milk in a small pot on the stove over medium heat to 110 degrees F. Milk will steam when ready. Do not boil. Remove the milk from the heat and sprinkle the yeast on top of the warm milk. let sit for 10 minutes until the yeast foams.
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Combine the flour, ¼ cup sugar, butter and egg in the bowl of a stand mixer. Allow the butter to cool before adding so it doesn’t cook the eggs. Attach the dough hook to the mixer.
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Turn the mixer on a low setting and slowly pour the warm milk mixture along the side of the bowl to incorporate. Scrape down the sides of the bowl if needed.
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The dough will form into a ball. Allow the machine to kneed the dough for about 5 minutes.
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In a clean bowl, coat the inside of the bowl with cooking spray or butter. Transfer the ball of dough to the bowl and cover with plastic food wrap.
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Set aside in a warm part of the kitchen for at least 1 hour, until the dough is doubled in size.
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When the dough has risen, grease a 12 cup nonstick muffin tin.
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Mix the blueberries, cornstarch and cinnamon in a small bowl. Set aside.
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Roll out the dough out on a lightly floured surface to about 12 inches by 15 inches rectangle. Sprinkle the remaining ¼ cup of sugar over the rolled out dough. Distribute the blueberry mixture evenly over the dough.
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Roll the dough into a tight coil and cut into 12 equal pieces. Place each piece cut side up in the greased muffin tin. Cover the tin with a tea towel and set aside for another hour to double in size again.
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Preheat your oven to 350 degrees F. Cook your muffins for 25 minutes until golden brown.
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Transfer the muffin tin to a cooling rack for 15 minutes.
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While the buns are cooling, combine the icing sugar, vanilla extract and milk in a small bowl. Add extra milk or icing sugar until you achieve the desired consistency.
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Set aside.
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Gently remove the buns from the muffin tin with a butter knife and transfer to a serving tray. Drizzle the glaze over top of the buns. Allow to cool for an additional 5 minutes before serving. Best served warm, still fabulous at room temperature.