Warm the milk to 110 degrees and add the yeast and 1 teaspoon of the sugar. Let the mixture sit until foamy, about 10 minutes.
Add the milk mixture, rest of the sugar, vanilla, egg yolks, and bread flour to a standing mixer with a bread hook attachment and knead for 3 minutes. Add in the room temperature butter cut into cubes. And continue to knead on medium speed for 5 minutes. Cover bowl and let rise for 45 minutes.
Pour canola oil into a large dutch oven about 3 inches high. Turn the heat to medium/high slowly heating up to temperature. Place a deep fry thermometer into the oil until it registers 360 degrees.
Gently roll the dough onto a well-floured surface until about ½ inch thick. With a 2-inch biscuit cutter, stamp out 12 circles and move to a tray and let proof about 10 minutes. It will be ready when you poke the side and it bounces back but still leaves an indentation.
Carefully place donuts into the hot oil releasing the dough away from your body. Fry each side of the dough until golden brown, about 1-2 minutes each.
Remove the donut and place directly into powdered sugar, toss until coated and place onto a cooling rack.
Make the Vanilla Custard
In a medium saucepan, heat the half and half. In a small bowl, whisk the egg yolks, vanilla, corn starch, and sugar together until smooth. Once the half and half starts to steam, do not let it come to a boil, slowly drizzle a ladle at a time into the yolk mixture while whisking. Transfer the mixture back into the saucepan and whisk until the mixture has thickened and sticks to the back of the spoon. Pour into a bowl and cover with plastic wrap directly onto the custard.
Let the custard come to room temperature before placing into a piping bag fitted with a filling attachment.
Poke a small hole in the side of each donut and fill with vanilla custard.
