Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until softened, about 10 minutes. Add Brussels sprouts and cook for 5 minutes more. Drain.
Preheat oven to 375 degrees F (190 degrees C). Grease a baking dish.
Beat heavy cream in a chilled glass or metal bowl with an electric mixer until soft peaks form. Beat eggs in a separate bowl until foamy, 2 to 3 minutes, and generously season with salt, pepper, and nutmeg. Stir in Cheddar cheese. Fold in whipped cream.
Place drained potatoes and Brussels sprouts in the prepared baking dish. Cover evenly with egg-cream mixture.
Bake in the preheated oven until top is lightly browned, 25 to 35 minutes.
