Warm the milk in a small saucepan until it bubbles, then remove from heat. Let cool until lukewarm.
In a small bowl, dissolve yeast in warm water. Let stand until creamy, about 10 minutes.
In a large mixing bowl, combine the yeast mixture, milk, sugar, eggs, butter, salt, and 2 cups of the flour. Stir well to combine. Stir in the remaining flour, ½ cup at a time, beating well after each addition. When the dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.
Place the dough in a lightly oiled bowl and turn to coat the surface. Cover with a damp cloth and let rise in a warm place until doubled in volume, about 1 hour.
Deflate the dough and turn it out onto a lightly floured surface. Roll out to ½ inch thickness. Cut into 3 inch squares. Place the squares on a lightly floured surface and let rise until doubled in volume, about 30 minutes.
Heat oil in a deep-fryer or large heavy skillet to 350 degrees F (175 degrees C). Fry doughnuts in hot oil until golden brown, turning once. Drain on paper towels. Roll the doughnuts in sugar while still hot.