Heat the milk in microwave until warm, but not hot, to the touch, about 110F-115F.
Sprinkle yeast into the water, and let bloom for 10 minutes, or until bubbly.
In a standing mixer, combine sugar, salt, eggs, vanilla extract, butter, and nutmeg, and whisk to combine slightly.
Add yeast mixture and about half of the flour. Begin mixing the dough with the bread hook. Add remaining flour, about 1/2 cup at a time, until all flour is incorporated. If dough is still sticky, continue adding flour about 2 tablespoon at a time until dough is not longer wet and sticky.
Knead dough for 4-5 minutes on medium speed. Dough should be smooth and should not be sticking to the sides of the bowl.
Grease a large bowl with cooking spray or vegetable oil, and place dough in bowl. Cover with plastic wrap or a clean kitchen towel and let rise in a warm spot until dough has doubled in size, about 1 to 1 1/2 hours. You can also let the dough rise overnight in the fridge (8 hours minimuif desired. If refrigerating overnight, let come to room temperature before working with the dough.
Punch down the risen dough, and roll it onto a clean work surface until it is 1/4 inch in thickness.
Using a biscuit cutter, cut dough into 3 inch circles.
Place circles onto parchment lined baking sheets, spacing them out generously to leave space for rising. Cover loosely with a clean kitchen towel until doubled in size, about 1 to 1 1/2 hours. Meanwhile, make the marshmallow filling.
Heat oil in a large dutch oven or deep fryer until 350F.
Fry doughnuts, about 2 at a time, for 1 minute on each side, until lightly golden brown. Remove with a slotted spoon.
Place doughnuts on paper towel lined plates or cooling racks and let cool slightly.
Toss in sugar, and let cool before filling.
To fill doughnuts, first make a hole in the side of the doughnut using either the handle of skinny wooden spoon or slender piping tip. Using a piping bag with a narrow piping tip, fill each doughnut with marshmallow creme. If you want to be really fancy, you can use a specialty piping tip made for piping creme filled doughnuts, but it isn't necessary to use this.
These are best the day that you make them, so serve immediately, and enjoy!