In a large bowl, whisk together flour, sugar, baking powder, salt and nutmeg. Make a well in the center.
In a large measuring glass, whisk together milk, egg, butter and vanilla extract. Pour into the center of the dry ingredients then mix with a large spoon. Stir until dough is combined but do not overmix. The dough will be sticky! Cover with plastic wrap and set the bowl in the fridge for 1 hour.
After and hour, remove dough and place on a well floured surface. Roll dough out to be about 1/2to 1 inch thick. Using a doughnut cutter, biscuit cutter or… something round, cut circles into the dough. To cut out the center, I used the bottom of an apple corer, but you can also use a bottle cap or something of the sort.
Heat oil in a large saucepan over medium heat so it’s about 2-3 inches deep. Once the oil hits 360-365 degrees, fry the doughnuts 2-3 at a time, for about 2 minutes per side, or until puffed and golden brown. Make sure you use a candy thermometer as this is the only way to determine the temperature! I have burned many doughnuts in my life. It is not pretty. Remove doughnuts with a slotted spoon and let cool on a paper towel. Repeat with remaining dough. Let the doughnuts cool slightly, then poke holes in the top of them, not going the whole way through, with a fork or something of similar size. Pour the tres leches glaze over top – I like to do this a few times. I go over the donuts ones, then let them sit for 5 minutes. Then go over them again and maybe once more. Serve immediately.