Warm the milk to around 105°F (lukewarm). Pour into stand mixer bowl fitted with dough hook. Add 2 tablespoons sugar and sprinkle yeast over the top. Stir gently and let sit for 10 minutes until foamy and bubbly.
Add flour, 1/2 teaspoon salt, beaten egg, and 50g neutral oil to the yeast mixture. Mix on low speed for 10-12 minutes until the dough is smooth and elastic. Test with the windowpane test - pinch off a small piece and stretch it thin enough to see light through without tearing.
Shape dough into a ball and place in a lightly greased bowl. Cover tightly with plastic wrap. Refrigerate for minimum 3 hours, preferably overnight (up to 24 hours maximum).
Remove chilled dough from fridge. Turn out onto very lightly floured surface. Roll out to 1/2 inch thickness, keeping it even throughout.
Cut out doughnuts using a 3 1/4-inch round cutter. Remove centers with a 1-inch cutter. Place each doughnut on individual parchment paper squares on a baking sheet. Gently press scraps together and cut more doughnuts, or cut into pieces for doughnut holes.
Cover shaped doughnuts loosely with a clean kitchen towel. Let rise at room temperature for 35-45 minutes until nearly doubled in size and puffy. Test by gently pressing with fingertip - should leave a small indentation that slowly springs back.
While doughnuts proof, mix the coating: combine 100g sugar, 1 tablespoon cinnamon, 1/2 teaspoon cardamom (if using), and pinch of salt in a shallow bowl. Set up a wire rack over a parchment-lined baking sheet.
Heat frying oil in a heavy-bottomed pot to exactly 350°F. Use a thermometer to monitor temperature constantly.
Test oil with a doughnut hole or scrap piece first. Gently lower 2 doughnuts at a time into hot oil, keeping them on parchment squares. The paper will release naturally after a few seconds - remove with tongs and discard.
Fry each doughnut for about 3 minutes total, flipping halfway through, until deep golden brown on both sides. Remove with slotted spoon and drain briefly on wire rack (about 30 seconds).
While still warm, toss doughnuts generously in cinnamon sugar mixture. The heat makes the sugar stick perfectly. Check oil temperature before frying next batch and adjust heat as needed.