Make the Custard:
Heat milk in a saucepan over medium heat until warm. In a bowl, whisk egg yolks, sugar, and cornstarch until smooth. Gradually add warm milk, whisking constantly. Return mixture to the saucepan and cook, stirring, until thickened. Remove from heat, stir in vanilla and butter, then let cool completely.
Prepare the Dough:
In a large bowl, mix flour, sugar, yeast, and salt. Add eggs and milk, stirring to form a dough. Add softened butter gradually and knead for 8–10 minutes until smooth. Cover and let rise for 1–1½ hours until doubled in size.
Shape and Fill:
Roll the dough into a rectangle on a floured surface. Spread the cooled custard evenly and sprinkle with chocolate chips. Roll tightly into a log and slice into 8–10 pieces. Place in greased muffin tins or a baking pan.
Second Rise:
Cover and let rise for 30–40 minutes, until puffy and airy.
Bake:
Preheat oven to 350°F (180°C). Brush tops with beaten egg and bake for 20–25 minutes or until golden brown.
Serve:
Dust with powdered sugar and serve warm. Enjoy your soft, creamy, and chocolatey brioches!