Trim sprouts, removing any damaged or yellowed leaves. Cutting through the core (top to bottom, not crosswise), slice about 1/4 thick.
Heat oil in a large heavy skillet. Add sprouts and stir to coat with oil. Grind a little pepper over sprouts. Don't salt yet, as the olives will add salt.
Cook, stirring frequently, until the sprouts are barely tender - 3 to 5 minutes. Don't overcook. Quickly stir in olives and tomatoes. Taste for seasoning; add salt if needed. Serve hot.