For the dough, add the milk, yeast, sugar and eggs to a bowl and blend slightly. Add the flour, salt and nutmeg and blend by hand or in a mixer fitted with the hook attachment. Immediately start adding the butter a bit at a time and continue to mix until the dough comes together. If using a mixer, continue to knead the dough until smooth and elastic, about 5 minutes and if mixing by hand, once the dough becomes to difficult to stir, turn it out onto a lightly floured surface and knead by hand until smooth and elastic. Place the dough into a lightly oiled bowl, cover the bowl with plastic wrap and let rise for at least 2 hours, or chill and let rise overnight.
For the ganache glaze, bring the cream up to a simmer and pour over the chopped chocolate. Gently stir this until the chocolate has melted, then stir in the oil and corn syrup. Set aside to cool to room temperature and chill until firm, about 2 hours, before using.
For the beignets, roll out the dough into a rectangle ¼-inch thick, about 18-x-15-inches. Cut the dough in half lengthwise and, on one half of the dough, spoon 18 teaspoonfuls of the ganache placing the spoonfuls about 2-inches apart, 6 across by 3 down. Cover this with the second piece of dough taking care to gently press down between the ganache to squeeze out the air around it. Trim the edges and cut into 18 beignets, each about 2-inches square. Place the beignets on a parchment-lined baking tray, cover with plastic wrap and let rise for 30 minutes.
Pour the oil into a tabletop deep fryer (following manufacturer’s instructions) or into a large, deep pot so that it is only filled about 3 inches. Heat the oil to 350F (use a candy thermometer if cooking beignets in a pot). Have a baking tray lined with paper towel, with a cooling rack placed over it. Place a beignet onto a slotted spoon and lower gently into the oil. Fit in as many beignets as you can, but with enough room that they have at least an inch between them. Fry the beignets for about 3 minutes, then flip over the fry for another 3 minutes, until an even golden brown. Use your slotted spoon to remove the beignets onto the cooling rack to drain and cool for at least 5 minutes before dusting with icing sugar and enjoying.
The beignets should be enjoyed warm or at room temperature on the day they are cooked.