METHOD
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mashed potatoes
Peel the potatoes, cut them into cubes, and add to a pot. Cover the potatoes with water and place over medium-high heat. Bring to a boil, then cook for 20 minutes or until soft. Drain and set aside for the steam to evaporate for approximately 5 minutes. While the potatoes are still hot, push them through a potato ricer, add the cold milk, and stir into a smooth puree. Set aside to cool to room temperature.
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potato buns
Add cooled mashed potatoes, flour, sugar, salt, yeast, lukewarm water, and lukewarm milk to a stand mixer bowl. Knead the dough in your stand mixer fitted with a dough hook attachment for 6 - 8 minutes. Optionally, use an electric mixer with the dough hook attachments. Add the egg yolk and butter and knead for 5 minutes. Cover the bowl with a kitchen towel or cling film and set aside to proof at room temperature for 60 - 90 minutes or until doubled in size.
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shape
Place the dough onto a floured surface. Using a sharp knife, divide the dough into 12 equal parts. Each should weigh approximately 80g / 2.8 oz. Take each piece of dough and roll it between your hands until you get a perfectly round ball. Place them on a large baking sheet lined with parchment paper. Make sure there's enough room in between the buns. Cover with plastic wrap and leave the buns to proof at room temperature for 45 - 60 minutes or until doubled in size. Preheat your oven to 190°C / 375 °F or your fan-assisted oven to 175°C / 350 °F.
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bake
Remove the cling film and brush the buns with egg wash. Create steam in your oven. You can spray some water into the oven before placing the baking sheet with the buns in the oven or place a roasting pan filled with 1 cup of water at the bottom of your oven. Then, place the baking sheet with buns on the middle rack and bake. Bake the burger brioche buns for 18 - 20 minutes at 190°C / 375 °F or in your fan-assisted oven at 175°C / 350 °F. Remove from the oven and transfer the buns to a wire rack to cool.