Make the brioche dough

• Warm the milk and combine it with the flour, sugar, yeast and salt in the bowl of a stand mixer.
• Mix in the eggs one at a time until a shaggy dough forms.

Knead in the butter

• Knead the dough with the dough hook, adding the softened butter a little at a time until fully absorbed.
• Keep kneading until the dough is smooth, elastic and pulls away from the bowl.

Let the dough rise

• Shape the dough into a ball, cover the bowl and leave it in a warm place until doubled in size.

Prepare the cookie dough filling

• Beat the remaining softened butter with the brown sugar and vanilla until creamy.
• Stir in the remaining flour and a pinch of salt, then fold in the chocolate chips until a soft cookie dough forms.

Shape and fill the brioche

• Roll the risen dough out on a lightly floured surface into a rectangle.
• Spread the cookie dough filling over the dough, leaving a border, then roll it up tightly.
• Place the roll in a greased loaf pan, cover and let it rise again until puffy.

Bake

• Brush the risen brioche with the beaten egg yolk.
• Bake in a preheated oven at 180 °C until deep golden and cooked through.

Cool and serve

• Let the brioche cool in the pan for a few minutes, then transfer to a rack.
• Slice and serve slightly warm so the cookie dough filling is gooey.