Warm 1¼ cups of whole milk until comfortably warm. Sprinkle 2¼ teaspoons of yeast into the milk and let it sit for 5 minutes until frothy.

In a large mixing bowl, combine the yeast mixture with 2 large eggs, 8 tablespoons of melted unsalted butter, ¼ cup of granulated sugar, and 1 teaspoon of salt. Gradually mix in 4 cups of all-purpose flour until a soft, slightly sticky dough forms.

Turn the dough onto a floured surface and knead for 5-7 minutes until smooth and elastic. Shape it into a ball and place in a greased bowl. Cover with a towel and let rise in a warm area for about 1 hour.

After rising, punch the dough down and roll it out to about ½-inch thickness. Cut out circles with a donut cutter, then remove centers with a smaller cutter. Place on a parchment-lined baking sheet and let rise for 30 minutes.

In a deep pot, heat vegetable oil to 350°F (175°C). Fry each donut for about 1 minute per side until golden brown, then transfer to a wire rack to cool.

In a saucepan, whisk together 2 cups of whole milk, ½ cup of granulated sugar, 2 large egg yolks, and ¼ cup of cornstarch. Cook over medium heat until thickened, then stir in 1 teaspoon of vanilla extract. Chill until cool.

For the glaze, heat ½ cup of heavy cream until simmering. Add 4 ounces of chopped chocolate and stir until smooth. Mix in 2 tablespoons of corn syrup and 1 teaspoon of vanilla extract.

Once donuts are cool, fill each with custard using a piping bag. Dip the tops into the chocolate glaze and let set before serving.