Make the batter for the Dutch baby by whisking together the eggs, flour, eggnog, sugar, cinnamon, and nutmeg until smooth.
Melt the butter in a 10” cast iron skillet over medium heat until just melted. Tilt pan to coat entire bottom of pan with melted butter, then pour batter into pan. Swirl pan to ensure batter forms an even layer across the whole pan, then transfer pan to oven. Bake at 425 degrees until well puffed and golden brown, about 12-15 minutes.
While Dutch baby bakes, make the sauce. Mix all ingredients for the cherry cranberry sauce together in a small saucepan until well combined. Place pan over medium heat and cook mixture, stirring occasionally, until fruit begins to break down and form a sauce, about 8-10 minutes.
The sauce and Dutch baby should be ready at about the same time. Once the Dutch baby is out of the oven, pour the cherry cranberry sauce into the center, and dust everything with powdered sugar. Serve immediately.