Sift the flour and Salt together. Stir in the yeast and caster sugar. Make a well in the centre of the bowl and pour in the milk with the eggs. Mix together to form a dough and, using your hands, beat the dough for 4-5 minutes. Using your hands knead in the softened butter, making sure it is well incorporated. Knead until the dough is smooth, shiny and elastic.
Lightly grease a 1.6 litre (2 ¾ pint) brioche mould. Pull a small amount from the dough and shape into a ball. Knead the larger piece into a round and drop into the mould.
Using two or three fingers, make a hole in the centre of the dough. Gently push the small ball of dough into the hole.
Mix together the egg yolk and milk for the glaze and brush a little over the brioche. Cover with lightly oiled cling film and leave to rise for 1½ - 2 hours or until the dough nearly reaches the top of the mould.
Meanwhile, preheat the oven to 230°C, 450°F, Gas 8. Brush the brioche with the remaining glaze and bake for 10 minutes. Reduce the oven temperature to 190°C, 375°F, Gas 5 and bake for a furhter 20-25 minutes, or until golden. Turn out onto a wire rack to cool.