In a stand mixer bowl fitted with a paddle, add flour, sugar, salt, and crumbled yeast, keeping salt and yeast separate. Mix briefly.

Add the beaten eggs and knead at medium speed for 2–3 minutes until the dough becomes thick and elastic.

Gradually add the diced butter while mixing at medium speed. Continue kneading for about 20 minutes until the dough is smooth, dense, and slightly sticky.

Transfer the dough to a clean bowl, cover with cling film, and let rise at room temperature for about 2 hours or until doubled.

Flatten into a thick rectangle, wrap tightly, refrigerate for 40 minutes to 2 hours, then freeze for 20 minutes to firm up.

Heat milk and butter in a saucepan over medium heat. Split the vanilla pod, scrape the seeds, and add both pod and seeds to the milk.

In a bowl, whisk yolks with sugar, then add flour and cornstarch until smooth.

Remove the vanilla pod and slowly pour the hot milk into the egg mixture, whisking constantly.

Return the mixture to the saucepan and cook over low-medium heat, whisking, until thick.

Transfer to a bowl, cover with cling film touching the surface, and refrigerate until cool.

Roll the chilled dough into a large rectangle about 8×12 inches (40×30 cm) on parchment paper.

Spread vanilla custard evenly over half of the dough lengthwise.

Sprinkle chocolate chips on top and gently press them into the custard.

Fold the empty half over the filled side and gently flatten to remove air bubbles.

Cut into 8 equal rectangles (1–1.5 inches wide).

Place on a lined baking sheet, cover, and let rise for 2 hours.

Preheat oven to 350°F (180°C).

Brush brioches with beaten egg and yolk.

Bake for 10–12 minutes until golden brown.

Meanwhile, boil sugar and water until dissolved to make syrup; let cool.

Brush hot brioches with syrup immediately. Cool completely before serving.