In a large mixing bowl, dissolve the yeast in warm milk and let it sit until foamy, about 5 minutes.

Add the eggs, melted butter, sugar, and salt. Mix until combined.

Gradually add the flour, mixing until the dough comes together. It should be soft and slightly sticky.

Knead the dough on a floured surface until smooth, about 5-7 minutes.

Place the dough in a greased bowl, cover with plastic wrap, and let rise in a warm place until doubled in size, about 1 hour.

Roll out the dough to ½-inch thickness on a floured surface. Cut out circles using a donut cutter or large round cookie cutter.

Cover the cut donuts with a kitchen towel and let rise for an additional 30 minutes.

Heat vegetable oil in a deep fryer or large pot to 350°F (175°C).

Fry the donuts in batches until golden brown, about 1 minute per side. Remove and let cool on a wire rack.

In a saucepan, whisk together milk, sugar, egg yolks, and cornstarch. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil.

Remove from heat and stir in vanilla extract. Cover with plastic wrap directly on the surface to prevent a skin from forming and chill in the refrigerator.

Heat the heavy cream in a small saucepan until it begins to simmer.

Remove from heat and add the chopped chocolate, letting it sit for 1 minute. Stir until smooth.

Stir in corn syrup and vanilla extract until the glaze is glossy.

Once cooled, make a small hole in the side of each donut. Use a piping bag fitted with a small nozzle to pipe the custard filling into the donuts.

Dip the top of each filled donut into the chocolate glaze. Let sit until the glaze sets.