In a large mixing bowl, combine 2.5 teaspoons of active dry yeast with 162.67 ml of room temperature whole milk. Let it sit for about 5-10 minutes until it becomes frothy.
In another bowl, whisk together 3 cups of all-purpose flour, 66.67 g of granulated sugar, and 2 teaspoons of kosher salt.
Once the yeast mixture is ready, add in 3 eggs and 7 tablespoons of softened unsalted butter, cut into pieces. Mix well until combined.
Gradually add the flour mixture to the wet ingredients, stirring until a dough begins to form.
Transfer the dough to a floured surface and knead it for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for about 1-1.5 hours, or until it doubles in size.
In a saucepan, heat 1 cup (366 ml) of whole milk and 100 g of granulated sugar over medium heat. In a separate bowl, whisk together 31.25 g of cake flour, 0.5 teaspoon of kosher salt, 4 egg yolks, and 1 teaspoon of vanilla extract. Once the milk is warm, slowly pour it into the egg mixture while whisking continuously.
Return the mixture to the saucepan and cook over medium heat, stirring constantly until thickened. Remove from heat and stir in 6 tablespoons of heavy cream. Transfer to a bowl, cover with plastic wrap, and refrigerate until cool.
Once the dough has risen, punch it down and turn it out onto a floured surface. Roll it out to about ½ inch thickness.
Using a cookie cutter, cut out the doughnut shapes and place them on a parchment-lined baking sheet. Cover and let them rise for another 30-45 minutes.
In a deep pot, heat 1 gallon of canola oil to 350°F (175°C).
Carefully place the doughnuts in the hot oil, frying a few at a time, until golden brown on both sides. Use a slotted spoon to transfer them to a cooling rack.
Once cooled, use a piping bag to fill each doughnut with the chilled vanilla cream filling.
Roll the filled doughnuts in 200 g of granulated sugar to finish them off beautifully.
