In a stand mixer, combine flour, sugar, salt, and yeast, keeping salt away from yeast initially.
Add beaten eggs and knead for 2–3 minutes until the dough becomes thick.
Gradually add softened butter while mixing, continuing to knead for about 20 minutes until smooth and slightly sticky.
Transfer dough to a bowl, cover, and let rise for 2 hours until doubled.
Flatten into a rectangle, wrap, and chill for at least 40 minutes (or up to 2 hours), then freeze for 20 minutes.
Prepare the custard:
Heat milk, butter, and vanilla pod until simmering.
In a bowl, whisk yolks, sugar, cornstarch, and flour.
Slowly pour hot milk into the mixture while whisking, then return to heat.
Cook until thickened, stirring constantly. Cool completely.
Assemble the brioches:
Roll chilled dough into a rectangle.
Spread custard over half the dough and sprinkle chocolate chips evenly.
Fold the dough over, seal edges, and cut into rectangles.
Place on a baking tray, cover, and let rise for 1 hour.
Bake:
Brush with egg wash and bake at 350°F (180°C) for 15–20 minutes until golden.
Brush with sugar syrup while warm for a glossy finish.
These Chocolate Chip Vanilla Custard Brioches are best enjoyed fresh and slightly warm.