In a large mixing bowl, combine 1 cup of whole milk, 1 cup of granulated sugar, and 1 cup of unsalted butter. Warm this mixture in the microwave until the butter is just melted and the sugar has dissolved. Allow it to cool slightly.
Next, sprinkle in 2 packets of rapid rise yeast and let it sit for about 5 minutes until it becomes frothy. This indicates that the yeast is activated.
Add 3 cups of all-purpose flour and 1 teaspoon of salt to the yeast mixture. Using a whisk or a wooden spoon, stir until the dough begins to come together. Once it’s too difficult to mix with a spoon, use your hands to knead the dough in the bowl until it is smooth and elastic.
Shape the dough into a ball and place it in a greased bowl. Cover it with a damp cloth and let it rise in a warm place for about 1 hour, or until it has doubled in size.
While the dough is rising, prepare the custard filling. In a medium saucepan, combine 1 cup of whole milk, 1 cup of granulated sugar, 1 tablespoon of cornstarch, and a pinch of salt. Whisk these ingredients together over medium heat until the mixture thickens and starts to bubble.
In a separate bowl, whisk together 1 large egg yolk and 2 egg yolks. Slowly add a bit of the hot milk mixture into the egg yolks to temper them, whisking constantly. Then pour the tempered egg mixture back into the saucepan and cook for an additional 2-3 minutes, stirring until thickened.
Remove from heat and stir in 1 tablespoon of unsalted butter and 1 teaspoon of vanilla extract. Allow the custard to cool before transferring it to a piping bag.
Once the dough has risen, punch it down and turn it out onto a floured surface. Roll it out to about ½ inch thick. Use a cookie cutter or round cutter to cut out donut shapes. Place the donuts on a floured baking sheet and cover them with a cloth. Let them rise for another 30 minutes.
In a deep frying pan, heat vegetable oil to 350°F (175°C). Carefully drop the donuts into the hot oil, a few at a time, being sure not to overcrowd the pan. Fry each donut for about 1-2 minutes on each side, or until golden brown.
Once cooked, remove the donuts with a slotted spoon and transfer them to a cooling rack to drain excess oil.
Once the donuts are cool, use the piping bag to fill each donut with the prepared custard. Insert the tip into the side of the donut and squeeze gently to fill it.
In a small saucepan, heat 1 cup of heavy whipping cream over medium heat until it begins to simmer. Remove from heat and add 4 ounces of semi-sweet chocolate chips. Let it sit for a minute, then whisk until smooth and glossy.
Dip the top of each filled donut into the chocolate glaze, allowing any excess to drip off. Place the glazed donuts on a cooling rack to set.