Add cream, milk and sugar to a small saucepan and bring the mixture to a simmer over medium heat stirring occasionally. Turn off the heat and let the mixture cool down to below 110°F.
Sprinkle active dry yeast over the liquid surface and let it bloom for 10 - 15 minutes, the mixture should puff up.
Add the flour and salt to a stand mixer bowl and stir to distribute. Add the yeast mixture to the flour mixture and knead with the dough hook on speed 2 for about 5 minutes.
Oil a glass bowl and your hands. Scrape the dough out of the mixing bowl and shape it into a ball in your hands and place it in the oiled bowl.
Cover, and let rise in a warm place for 1 - 2 hours until at least more than double in size.
Turn the dough out onto a lightly floured surface and roll out to about ½” thick. Use a 3” round cookie cutter to cut out the donuts and use a 1 ½” round cookie cutter to cut out the donut holes.
Reshape the dough including the donut holes into a ball and let it rest for about 10 - 15 minutes before you roll it back out and again and cut into more donuts. Continue to do this until you have cut out all of the donuts. Or leave the donut holes if you’d like.
Heat the oil in a heavy pot to 360°F, use a thermometer to monitor the temperature during frying as you may need to adjust the heat, try to keep the temperature between 350°F - 375°F.
Drop 3 - 4 donuts into the hot oil, depending on the size of your pan, and fry until golden brown, flipping the donuts halfway through cooking. Don’t crowd the pot.
Remove the donuts from the hot oil and rest them on a wire rack placed over a baking sheet to drain excess oil or simply place them on some paper towels to absorb the excess oil.
To make the vanilla glaze, whisk together powdered sugar, salt, vanilla extract and milk in a small mixing bowl until smooth.
To make the chocolate glaze, whisk together powdered sugar, cocoa powder, salt, vanilla extract and milk in a small mixing bowl until smooth.
Dip the donuts into the glaze of your choice and place them on a wire rack placed over a baking sheet to allow excess glaze to drip off.
This recipe makes 10 donuts if you reshape the donut holes. You can leave the donuts holes if you wish but this will reduce the amount of whole donuts.
When reshaping the dough to cut out more donut, you’ll need to allow the dough to rest to relax the gluten or it will shrink back on itself when cut.