Combine the yeast, milk and 1tbsp of the sugar in a small bowl. Set aside for 5 minutes or until frothy. Combine flour, salt and remaining sugar in a large bowl and make a well in the centre.
Pour yeast mixture and eggs into well. Stir until just combined (dough will be slightly sticky). Turn onto a well-floured surface.
Knead for 5 minutes or until dough is smooth and elastic.
Add butter, 2-3 pieces at a time, kneading well after each addition for 15-20 minutes.
Transfer to a greased bowl. Cover. Set aside in a warm spot until doubled in size.
Grease a baking tray with butter. Sprinkle with extra flour to lightly coat.
Knead dough for 2-3 minutes or until smooth. Divide the dough evenly into 12 portions.
Roll each portion into a smooth ball. Place on tray, leaving room for spreading.
Set aside in a warm spot until double in size. Preheat oven to 200°C/180°C fan forced.
Gently brush each brioche bun with extra egg.
Bake for 15 minutes or until golden brown and cooked through.
Serve warm or at room temperature.