Heat olive oil in a skillet over moderate heat.
Place the Brussels Sprouts into the skillet, flat side down. Cook until flat side is golden brown, approx. 5-7 minutes.
Turn the sprouts over and cook for another 5-7 minutes. At that point, the sprouts should be tender enough to pierce with a fork.
In the meantime, stir the curry powder and brown sugar into the melted butter and beat with a fork until thoroughly blended.
Once the Brussels Sprouts are tender, add the butter and shallots to the skillet and toss to coat.
Simmer over low heat until the shallots are tender, approx. 5 minutes.
At this point, you can add more butter if you wish.
Transfer the Brussels Sprouts to a serving dish and sprinkle with the toasted walnuts.