Step 1

Combine the warm water, milk, sugar, and yeast in a large bowl. Whisk to dissolve the yeast. Allow the yeast to proof for about 5 minutes or until it starts to foam.

Step 2

Add the remaining ingredients. Knead on low using a dough hook on your mixer or by hand. Knead for about 5 minutes or until the dough is nice and smooth.

Step 3

Place the dough into a greased bowl, cover with plastic wrap and let rise in a warm draft-free place until almost doubled in size, about an hour.

Step 4

Punch the dough down and roll out on a lightly floured surface to 1/2-inch thick. Use a 3-inch cutter to cut the donuts. Place the donuts on a floured parchment-lined baking sheet, cover with plastic wrap, and let proof for 15 minutes. Re-roll the remaining dough, cut out the remaining donuts and add them to the baking sheet.

Step 5

Heat 2 inches of oil in a heavy pot (Dutch oven) to 350-360°F. Drop 2-3 donuts at a time and allow to become golden before turning to the other side, about 2 minutes per side.

Step 6

Remove from the oil and place on paper towel-covered wire rack. Let cool before filling.

Step 7

For the pastry cream, add the sugar, cornstarch, and milk to a large saucepan and mix until smooth. Cook, stirring continuously, over medium heat until mixture begins to thicken and boil. Reduce heat to medium and simmer for 1 minute. Remove from heat.

Step 8

Add a little bit of mixture to the egg yolks and whisk together, then add egg mixture to milk mixture. Place the saucepan back on the heat and bring to a light boil. Allow to boil for 2 minutes, stirring continuously.

Step 9

Remove from heat, add butter and vanilla. Stir until smooth. Pour into a medium bowl. Cover with plastic wrap and press it directly on surface. Refrigerate until cold.

Step 10

For the chocolate glaze, heat the cream in a microwave or over the medium heat until just below boiling point. Pour the heated cream over the chocolate chips and let sit for 1 minute. Whisk it all together until the chocolate it fully melted.

Step 11

Fill a piping bag with a round tip with the cream. Using a small knife, cut a hole in the side of each donut about 3/4 of the way into the donut and pipe a generous amount of vanilla cream into the center of the donut.

Step 12

Swirl the top of the donut in the glaze and allow to sit for about 10 minutes before serving.