Place flour and yeast in a mixer bowl fitted with the dough hook and mix. Add sugar and margarine. Continue mixing until the margarine is completely crumbled into the flour. Add eggs and vanilla extract and mix again.

Add one cup of water and knead at slow-to-medium speed for eight minutes until the dough is soft and smooth. Add cognac towards the end of mixing.

Grease the walls of the mixer bowl. Cover the bowl with a greased plastic and let the dough rise until it doubles in bulk. Punch down, knead and let it rise again.

Divide the dough into two equal parts and form each part into a ball, with the edges gathered towards the center of the bottom of the ball.

Flour your work surface. Roll each dough ball half an inch (one and a half centimeters) thick. Use a round doughnut cutter shape two and a three-quarters inches (seven centimeters) in diameters. Cut shapes in the dough. Remove the inner circles and set aside

Arrange the doughnut rings on lined, greased cookie sheets. Cover loosely with plastic and let rise for 15 minutes.

Heat oil at least two inches high for deep frying in a wide, shallow pot that can easily hold the doughnuts. The oil temperature should not be above 325 degrees.

Fry the doughnuts until just golden, flip over, and fry on the second side. Remove the doughnuts from the oil with a slotted spoon and lay on a tray lined with paper towels.

To prepare the icing, place the chocolate pieces in a bowl. Heat the parve whipping cream and pour over the chocolate pieces. Wait one minute and mix well until the chocolate is melted. If the chocolate doesn’t melt completely, place the bowl in the microwave for a few seconds to finish melting. Add chocolate liqueur and mix well.

Now it’s time to ice the doughnuts. Dip each doughnut into chocolate icing. Wait about 30 seconds (not more) and decorate as desired. Your doughnuts will look elegant and festive!

Fry the “holes” from the doughnut for about 30 seconds on each side until golden. Place on a tray and sprinkle with confectioners’ sugar. Before you turn around, they’ll be gone — guaranteed!

These doughnuts freeze beautifully and retain their shape and airy texture. They freeze better without the icing. Remove as many as you need at a time from the freezer and heat in the microwave, and they taste fresh out of the pan. Decorate as needed just before serving.

Adding the cognac or brandy is very important because it makes the doughnuts absorb less oil during frying. Add it only towards the end of the kneading so the yeast will stay potent and retain its rising power.

For dairy doughnuts, you can substitute milk for the water and butter for the margarine and use heavy cream for the icing. The results are beyond delicious.

For successful doughnut frying, use a wide, shallow pot that will easily accommodate the doughnuts and enable easy access when you have to flip them over.

The oil should not exceed 325°F (170°C). If you don’t have a cooking thermometer, put a small piece of dough into the hot oil and see if a gentle bubbling forms around it. If there isn’t enough bubbling, wait until the oil gets hotter. If there’s too much bubbling, turn off the flame and allow the oil to cool, or add some cool oil from the bottle.

You can reuse the oil from the frying: Allow it to cool, line a strainer with paper towels, and place a bowl underneath it. Pour the oil into the strainer. All the black pieces in the oil will remain on the paper towel and you’ll have clean, clear oil. Transfer with a funnel into an empty oil bottle and store in the refrigerator until you’re ready to fry again.

For safety, always fry on a back burner, not in the front. Keep children away from the stove. Gently place the doughnuts in the pot — don’t throw them in. Make sure your hands are dry when forming the doughnuts; if necessary, grease them with a bit of oil.