Put the flour into a large mixing bowl, crumble the yeast over it, add sugar, salt, eggs, milk and the softened butter in small pieces. Knead with the dough hooks of the hand mixer for approx. 10 minutes on medium speed to a smooth dough.
Put the dough into a bowl and let it rise covered for about 1 hour. Cover the bowl with foil and leave to cool overnight.
Halve the dough the next day. Form one half of the dough into a ball on a floured work surface. Spread a large brioche mould (1 1/2 litre capacity) with fat and sprinkle a thin layer of flour over it.
Place the ball in the mould. Cover with a damp tea towel and leave in a warm place for about 2 hours. The volume must have doubled.
For the small brioches, divide the dough into 12 portions (each weighing almost 50 g). Remove 1 small ball the size of a marble from each portion of dough. Shape the larger balls. Grease 12 brioche moulds (each containing approx. 100 ml) and dust with flour.
Place larger balls in the moulds and place the small balls on top. Now let the small brioches rise for 1 1/2 - 2 hours until their volume has doubled.
Mix the egg yolks with 1 teaspoon of water and brush the surface of the bread with it. Sprinkle with sugar crystals. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for about 20 minutes.
Spread the rolls with egg yolk mixture and sprinkle with sugar crystals. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 10-15 minutes.
Allow both types of brioche to cool for about 10 minutes each, then carefully remove them from the mould and let them cool on a cake rack. Cut bread into 12 slices.