In a mixing bowl, mix warm water, active dry yeast, and 1 teaspoon of the granulated sugar. Let the mixture sit for 5 minutes until it becomes frothy.
Stir in the remaining granulated sugar, eggs, warm milk, melted butter, and salt. Gradually add all-purpose flour while stirring until a dough begins to form.
Turn the dough onto a lightly floured surface and knead it for several minutes until smooth and elastic.
Shape the dough into a ball, cover with a clean towel, and let it rise for about 1 1/2 hours until doubled in size.
Roll the dough on a floured board to about 1/4 inch thick and cut out donut shapes using a donut cutter.
Place the cut donuts on parchment paper and allow them to rest and rise for an additional 30 minutes.
Meanwhile, heat Canola oil in a heavy pan to 375°F.
Fry the donuts in batches for 2-3 minutes on each side until golden brown.
Remove them with a slotted spoon and let them drain on paper towels.
Optionally, while still warm, toss the donuts in granulated sugar or coat them with glaze.
