Preheat the oven to 350 degrees F (175 degrees C). Place 4 ramekins or custard cups into a shallow baking dish; add enough water to come halfway up the sides of the ramekins.

Heat eggnog in a pan over medium heat; cook and stir occasionally until simmers, about 10 minutes.

Meanwhile, beat egg yolks and sugar together in a mixing bowl until light colored and frothy. Stir in mascarpone until well blended and smooth; whisk in 1/4 cup heated eggnog. Gradually whisk in remaining eggnog. Pour custard through a fine-mesh-sieve to remove any egg strands. Stir in vanilla extract, nutmeg, and cinnamon. Pour into the prepared ramekins, dividing evenly.

Bake in the preheated oven until custard set, 30 to 45 minutes. Centers should wiggle slightly when shaken, but not be soupy.

Remove from oven and cool 30 minutes; refrigerate at least 3 hours before serving.