Add the melted butter to the remaining milk. Combine the milk mixture with the egg yolks, salt and the yeast mixture. Stir in half the flour and mix well. Mix in the remaining flour and knead until the dough is smooth and elastic and starts to pull away from the bowl. The dough should be a bit sticky.
Form the dough into a ball and place in a large bowl sprayed with nonstick cooking spray. Cover the bowl with plastic wrap and let rise in a warm place until doubled in bulk, about 45 minutes. (I preheat my oven to 200 degrees and then turn it off.)
After dough is doubled in size, punch down and place dough on lightly floured surface. Roll dough out to 1/2 inch thick. Using a 3-inch circle, cut out doughnuts. Re-roll scraps.
Line 2 large baking sheets with parchment paper. Place 12 doughnuts on each sheet. Cover doughnuts with kitchen towels and let rest for about 30 minutes.
Pour enough canola oil, about 1-2 quarts, into a large heavy bottomed Dutch oven so it's a few inches deep, set over medium-low heat. When oil is hot enough, add 4 doughnuts at a time and cook for about 2 minutes per side until golden. Remove doughnuts from oil with a slotted spoon and place on a rack over a large baking sheet. Repeat with remaining doughnuts.
Sprinkle warm doughnuts with confectioners' sugar. Serve warm.