Warm 1 cup (240ml) of whole milk to 110°F (43°C). Whisk in 2.25 tsp (7g) of active dry yeast and let sit for 5-10 minutes until frothy.

In a stand mixer, combine 3 cups (360g) bread flour, 1/4 cup (50g) sugar, salt, the egg, and softened butter. Pour in the yeast mixture and knead on medium speed for 8 minutes until smooth and elastic.

Transfer the dough to a lightly oiled bowl, cover tightly, and let rise in a warm spot for 1 hour until doubled in size.

Whisk 4 egg yolks, 1/2 cup (100g) sugar, and 3 tbsp (24g) cornstarch in a bowl until pale. Heat 1.5 cups (360ml) whole milk in a saucepan until simmering.

Slowly drizzle the hot milk into the yolk mixture while whisking. Return everything to the saucepan and cook over medium heat for 3-5 minutes until very thick. Stir in vanilla, then cover with plastic wrap touching the surface and chill completely.

Punch down the dough and roll to 1/2-inch (1.25cm) thickness. Cut 3-inch (7.6cm) rounds and let them rest on parchment paper for 45 minutes.

Heat oil to exactly 350°F (175°C). Fry the dough rounds for 2 minutes per side until they form a golden-brown deep-fried crust. Drain on white parchment paper over a wire cooling rack.

Place 1 cup (170g) chocolate chips and corn syrup in a bowl. Pour 1/2 cup (120ml) hot heavy cream over the chocolate. Let sit for 5 minutes, then whisk until it forms a heavy, glossy dark brown glaze.

Poke a split in the side of each cooled donut. Pipe the thick pale yellow vanilla custard inside until slightly oozing. Dip the top half in the chocolate glaze and return to the wire cooling rack so it slightly drips down the sides.