For the cream: In a large saucepot bring 500 milliliters (2 cups 2 tablespoons) of the milk to a boil, and cook to scald the milk. Combine the sugar and eggs in a large mixing bowl. Slowly add the hot milk to the egg mixture to temper the eggs. In small bowl, combine the cornstarch and the remaining 250 milliliters (1 cup) milk. Return the egg mixture to the saucepot and add the cornstarch mixture. Cook until the cornstarch flavor cooks out and the mixture thickens, 20 minutes. Remove from the heat and mix in the peppermint extract.
For the beignets: Combine 2 cups warm water, the sugar and yeast, and set aside. In the bowl of a stand mixer fitted with the dough hook, mix the heavy cream, melted butter and eggs. Add the yeast mixture and mix just to combine. Add the flour, nutmeg and salt. Mix until the gluten forms, about 10 minutes. Remove the dough from the bowl, roll it out to 1/4-inch thick, and then cut into 1-inch squares, 36 total. Proof the dough in a warm place until almost doubled in size, about 2 hours.
In a large, shallow pan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F. Fry the beignets until golden brown on both sides.
Serve the beignets with a side of peppermint cream.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.