Prepare the Dough:

1. Warm the Milk: Heat the milk until warm, but not hot. You should be able to comfortably dip your finger into it.
2. Activate the Yeast: Dissolve 1/4 cup of sugar in the warm milk. In a small cup, add the yeast and pour the milk-sugar mixture over it. Stir gently and let it sit for 10 minutes until frothy.
3. Mix Wet Ingredients: In a separate bowl, combine the beaten eggs with the melted butter, stirring constantly until well incorporated.
4. Combine Mixtures: Pour the yeast mixture into the butter and egg mixture, whisking constantly until thoroughly combined.
5. Incorporate Flour: Slowly start adding the flour and salt to the wet mixture, whisking or stirring constantly. Continue to mix for about 10 minutes until the dough starts coming together.
6. Knead the Dough: If the dough is sticky, add a bit more flour. Knead the dough gently on a lightly floured surface until you have a springy, smooth dough.
7. First Rise: Transfer the dough to a lightly oiled bowl, cover with plastic wrap, and let it sit for about 30 minutes at room temperature.
8. Refrigerate the Dough: After the initial rise, transfer the dough to the fridge and refrigerate for at least 8 hours, or overnight.

Shape and Rise:

1. Prepare the Doughnuts: Remove the bowl from the fridge and turn out the dough onto a lightly floured surface. Roll the dough out to 1/4 to 1/3-inch thickness.
2. Cut the Dough: Using a 3-inch cutter (or a glass), cut as many rounds as possible. Use a 1 1/2-inch cutter (or small bottle cap) to cut holes in each round.
3. Second Rise: Place the doughnuts and holes on a floured baking sheet. Cover with a large tea towel and place in a warm spot. Let them rise undisturbed for at least an hour until visibly puffier.

Fry the Doughnuts:

1. Heat the Oil: In a large pot, heat enough oil to fry the doughnuts. The oil should be hot but not too hot, or the doughnuts will burn. Test with a small piece of dough; it should sizzle and rise to the surface slowly.
2. Fry Doughnuts: Fry the doughnuts in batches, 1-2 at a time, cooking for about 1 minute on each side until golden brown. Remove with a slotted spoon and drain on paper towels.
3. Fry the Holes: Fry the doughnut holes next. They will cook faster, about 30 seconds per side.

Glaze and Coat:

1. Prepare the Glaze: In a small pan, combine 1/2 cup of sugar with just enough water to submerge it. Add a dash of cardamom. Cook over medium heat until the sugar dissolves and thickens to a syrupy consistency.
2. Glaze the Doughnuts: Brush each doughnut with the syrup while still warm. For an extra treat, dip the glazed doughnuts in a mixture of granulated sugar and cinnamon.

Serve:

1. Serve Warm or at Room Temperature: These doughnuts are best served warm, but they can be enjoyed at room temperature as well.