Place Brussels sprouts into a pot, cover with water, and bring to a boil. Cook until tender yet firm to the bite, about 15 minutes. Drain.
Melt butter in a saucepan over medium heat while Brussels sprouts are cooking and cook onion until soft and translucent, about 5 minutes. Pour in white wine and bring to a boil. Stir in cream, nutmeg, and pepper. Add Edam cheese and stir until melted. Add drained Brussels sprouts and heat in cheese sauce over low heat, about 5 minutes. Season with salt.