Preheat the oven to 350°F (175°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 it 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 of heated eggnog. Gradually whisk in the 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 the custard sets, 30 to 45 minutes. Centers should wiggle slightly when shaken, but not be soupy.