Add the milk and water to a saucepan over low heat and heat until just warmed.
Place the butter in the bowl of your electric mixer and pour the warm milk over the butter, stirring until it melts. Add in the honey and sprinkle the yeast over top, giving it a quick stir. Let sit for 5 minutes or so until the yeast is foamy.
Add the eggs, sugar, salt, nutmeg and half of the flour to the yeast mixture. Using the paddle attachment, beat the dough on low speed until combined and sticky. Add in the remaining flour and beat on low speed, gradually increasing to medium speed until the dough comes together. It will still be stick! Switch to a dough hook and beat the dough for 5 minutes on medium speed, or until it is pulling away from the sides of the bowl.
Remove the dough from the mixing bowl and place it in another oiled bowl to rise. Cover and let it rise in a warm place for one hour.
Place the dough on a floured surface and roll it out to be 1-inch thick. Use a 1-inch biscuit cutter (or something larger if you prefer) to cut out the dough rounds and a smaller circle (I used a cap to a bottle of Baileys) to cut out the center. Place the rounds on a baking sheet, cover, and let rise again for 30 minutes or so.
Heat a large pot of oil (I used vegetable oil) over medium heat. Use a candy thermometer to determine the temp – you don’t want it to be higher than 365-370 degrees. Add the donuts 2 or 3 at a time and fry for about 1 minute per side. Remove with a large slotted spoon and place on a paper towel to drain. Let cool completely.