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Put the milk in a small bowl. Add the yeast and a pinch of sugar, stir to dissolve and leave for 5–10 minutes until foamy.
In a large bowl, whisk together the flour, caster sugar and salt. Make a well in the centre.
Lightly beat 2 of the eggs. Pour into the well along with the yeast mixture. Mix on low speed until just combined, then knead for 10–15 minutes until the dough is elastic.
Gradually add the cubed butter, kneading for another 10–15 minutes until the dough is smooth, shiny and passes the windowpane test.
Shape the dough into a ball and place in a greased bowl. Cover with cling film or a clean tea towel and prove in a warm place for 1½–2 hours, or until doubled in size.
Knock back the dough with your knuckles, cover and chill in the fridge for at least 2 hours or overnight.
Divide the dough into equal pieces and braid them or place the pieces in a greased loaf tin. Cover and prove for 1–1½ hours, or until nearly doubled.
Meanwhile, preheat the oven to 180°C (160°C fan)/gas mark 4. Beat the remaining egg.
Brush the surface of the brioche with the beaten egg and bake for 25–35 minutes, until golden and hollow-sounding when tapped on the base.
Turn out the brioche and cool completely on a wire rack before slicing.