1. Prepare the Dough: In a mixer bowl, combine the flour, sugar, salt, and crumbled yeast (making sure the salt and sugar don’t touch the yeast). Mix briefly.
2. Add the Eggs: Mix for 2-3 minutes at medium speed until the dough thickens.
3. Add the Butter: Gradually incorporate the softened butter in small additions, kneading at medium speed. Continue kneading for about 20 minutes until the dough becomes smooth and slightly sticky.
4. Let it Rise: Transfer the dough to a clean bowl, cover with cling film, and let it rise in a warm place for about 2 hours, or until doubled in size.
5. Chill the Dough: Flatten the dough into a thick rectangle, wrap it in cling film, and refrigerate for 40 minutes to 2 hours. If needed, place it in the freezer for 20 minutes.

For the Vanilla Custard (Crème Pâtissière):

1. Heat the Milk: In a medium saucepan, heat the milk and butter with the vanilla pod and its seeds over medium heat.
2. Whisk the Egg Yolks: In a separate bowl, whisk the yolks with the sugar, then add the flour and cornstarch. Whisk until smooth.
3. Combine the Mixtures: When the milk starts bubbling, remove the vanilla pod and pour the hot milk slowly over the egg mixture, whisking continuously.
4. Thicken the Custard: Return the mixture to the pan and cook over low-medium heat, whisking constantly until it thickens. Transfer to a bowl, cover with cling film (making contact with the custard), and refrigerate until needed.

For the Filling and Assembly:

1. Roll Out the Dough: On a floured surface, roll out the chilled dough into a large rectangle (8×12 inches / 40×30 cm).
2. Add the Custard and Chocolate Chips: Spread vanilla custard over half of the dough lengthwise. Sprinkle the chocolate chips over the custard and gently press with a rolling pin to ensure they stick.
3. Fold and Cut the Dough: Fold the empty side of the dough over the custard-covered side, gently flattening to remove air bubbles. Using a sharp knife, cut the dough into 8 equal rectangles (about 1 to 1.5 inches wide).
4. Let Them Rise: Place the rectangles on a parchment-lined baking sheet, cover with cling film, and let rise for 2 hours.

For the Syrup and Brushing:

1. Prepare the Syrup: In a small saucepan, bring sugar and water to a boil until the sugar dissolves. Set aside to cool.
2. Bake the Brioches: Preheat the oven to 350°F (180°C). Brush the brioches with the beaten egg and yolk. Bake for 10-12 minutes or until golden brown.
3. Brush with Syrup: Immediately after removing from the oven, brush the brioches with the prepared syrup. Allow them to cool completely before serving.