Warm the Milk (1 1/2 cup) to around 115 degrees F (45 degrees C). Add to a small bowl, add the Granulated Sugar (1 pinch) and sprinkle over the Instant Dry Yeast (1 3/4 teaspoon).
Allow to stand for around 5 minutes or until the yeast begins to foam.
In the meantime, combine the remaining Granulated Sugar (1/3 cup), Unsalted Butter (1/2 cup), Egg (2) and Salt (3/4 teaspoon) in the bowl of a stand mixer with the dough hook attached.
Add the yeast mixture and mix on a low speed until just combined.
Add the All-Purpose Flour (5 cup) and mix on a low speed until the dough just comes together.
Turn the speed up to medium and continue kneading.
Knead for 5 minutes until the dough is smooth and elastic.
Place the dough in an oiled bowl and cover with plastic wrap. Leave it in a warm place to rise for about 2-3 hours.
The dough should have doubled in size by now, which is a good sign that it has proven properly
Remove the dough from the bowl, place it on a floured surface and punch down.
Roll it out to a 1/2 inch thickness.
Using a floured doughnut cutter, begin cutting out your doughnuts.
Place doughnuts on a floured baking sheet, with a few inched between them. Cover with a clean tea towel and place in a warm place to double in size, around 30 minutes.
Begin heating the Vegetable Oil (as needed) in a medium-size dutch oven fitted with a thermometer on the side. Allow it to come up to around 350 degrees F (180 degrees C).
Begin frying your doughnuts in batches, for around 2-3 minutes on each side, or until nicely puffed and golden.
Remove from the oil and place on a cooling rack covered with kitchen towel, to soak up any excess oil. Allow to cool completely while you begin making the glaze.
Combine the Heavy Cream (4 tablespoon) and Powdered Confectioners Sugar (220 gram) in the bowl of a stand mixer fitted with the balloon whisk. Mix on a high speed until just combined.
Add the Salt (1/2 teaspoon) and Vanilla Extract (1/2 teaspoon) and continue mixing on high until the glaze is completely smooth.
Begin dipping each doughnut into the glaze and gently swirl.
Twisting the doughnut out of the bowl, allow excess glaze to drip off the doughnut and place back on to the wire rack to set for about 30 minutes.