In a bowl combine milk, 50 ml / 1.8 oz water, active dry yeast, and sugar. Set aside and let the yeast mixture rise for about 10 minutes.TipThe water should not be too hot or it will kill the yeast. Make sure it has around 35°C / 95 °F.
In a bowl (or in a bowl of a stand mixer, fitted with a dough hook) combine all-purpose flour and salt. Add the yeast mixture and stir to combine well, using a spatula. Using your hands, knead into a nice, smooth dough. Knead for about 5 minutes by hand or 2 - 3 minutes in a stand mixer. Add cubes of softened butter and knead the butter into the dough, until they are no more visible pieces left. Knead for about 5 minutes by hand or 3 - 4 minutes.
let the dough rise
Cover the bowl with a plastic wrap or a kitchen towel. Leave the dough to rise at room temperature for about 60 minutes or until doubled in size.
shape and proof
Lightly flour the dough and transfer it to a clean work surface. Divide the dough into 8 equal parts, using a metal dough scraper or a sharp knife. Take each piece of dough and roll between your hands until you get a perfectly round ball. Place on a large baking sheet lined with parchment paper. Make sure there's enough room in between the buns. Gently brush each bun with egg wash. Cover with plastic wrap and leave the buns to proof at room temperature for 50 minutes or until doubled in size. Preheat your oven to 200°C / 395 °F.
Remove the plastic wrap and lightly brush the buns for the second time. Sprinkle with sesame seeds. Create steam in the oven. You can either spray some water into the oven before placing the baking sheet with buns in the oven or you can place a roasting pan filled with 1 cup of water to the bottom of your oven. Then place the baking sheet with buns on the middle rack and bake. Bake the burger brioche buns for about 15 minutes at 190°C / 375 °F, then carefully remove the roasting pan with water and continue to bake for another 10 minutes or until golden brown. Remove from the oven and transfer the buns to a wire rack to cool.
Eat or Store
Eat the buns right away or store them in a freezer bag and freeze for up to 3 months.