In a heat-proof bowl, whisk together the eggs, egg yolk, sugar, cornstarch, and cake flour until smooth. Gradually pour in tempered steaming milk while whisking continuously. Transfer to a saucepan and cook over medium-low heat, whisking until thickened (about 5 minutes). Stir in butter and vanilla. Chill until firm.

In a stand mixer, combine bread flour, cake flour, sugar, sweetened condensed milk, cold water, and cold milk. Add half of the egg and yeast. Mix on low speed until shaggy dough forms (about 5 minutes). Rest for 30 minutes.

Sprinkle sea salt over the dough and knead briefly. Gradually add butter cubes, kneading until smooth and elastic (about 10 minutes). Cover and let rise in a warm place until doubled in size (about 1 to 1.5 hours).

Punch down the risen dough, divide into 8 pieces. Flatten each, add custard in the center, seal edges tightly. Place on parchment-lined baking sheet, seam side down.

Cover with a damp towel and proof in a warm place for about 1 hour until they puff up slightly.

Preheat oven to 375°F (190°C). Brush tops with egg wash. Optionally, pipe custard on top or sprinkle with pearl sugar. Bake for 12-15 minutes until golden brown. Allow to cool slightly before enjoying.