In a medium bowl, dissolve the yeast in the warm water.
Add the milk, margarine or butter, egg, sugar, and salt, and blend with an electric mixer until smooth
Add half the flour and mix for 30 seconds.
Add the remaining flour and knead the dough with flour-dusted hands until smooth.
Cover the bowl of dough and leave it in a comfy, warm place until the dough doubles in size, about 1 hour. You can tell that the dough has risen enough when you poke it with your finger and the indentation stays.
Rollout the dough on a heavily floured surface until it’s about 1/2 inch thick.
If you don’t have a donut cutter, and don’t intend to buy one, here’s a way to punch out your dough: Empty a standard 15-ounce can of whatever you can find-vegetables, refried beans, even dog food. Be sure to wash out the can very well, and punch a hole in the opposite end so that the dough won’t be held inside the can by a vacuum.
When you’ve punched out all the dough (you should have about a dozen unholed donuts),
it’s time for the holes. Find the cap to a bottle of lemon juice or Worcestershire sauce, or any other small cap with a diameter of about 1 1/4 inches. Use this to punch out holes in the center of each of your donuts.
Place the donuts on plates or cookie sheets, cover, and let stand in the same warm, comfy place until they nearly double in size. This will take 30 to 45 minutes.
Heat the vegetable oil in a large frying pan over medium heat.
Bring the oil to about 350 degrees. It is easily tested with scrap dough left over from punching out the donuts. The dough should bubble rapidly.
Fry each donut for about 30 seconds per side, or until light golden brown. Cool 5 minutes on paper towels.
For either the plain or the chocolate glaze, combine the margarine or butter with the powdered sugar in a medium bowl and blend with an electric mixer.
Add the vanilla and hot water. Mix until smooth.
If you’re making the chocolate glaze, melt the chocolate chips in a microwave-safe bowl in the microwave for 30 to 40 seconds. Stir, then microwave another 30 seconds and stir again until completely melted.
Add to the plain glaze mixture. Blend until smooth.
When the donuts have cooled, dip each top surface into the glaze and then flip over and cool on a plate until the glaze firms up, about 15 minutes.