Wash the Belgian endives and remove any damaged outer leaves. Cut each endive in half lengthwise.
Heat the olive oil (or butter) in a skillet over medium heat. Add the Belgian endives, salt, and black pepper.
Sauté for about 5 minutes, turning the endives occasionally until they begin to brown.
Add the nutmeg, minced garlic, and brown sugar. Cook for an additional minute, turning the endives once.
Add the water, reduce heat slightly, and cook until the endives are tender (about 10 to 15 minutes). Turn them gently from time to time to ensure even cooking without breaking the leaves apart.