Trim and discard stem ends from brussels sprouts; rinse sprouts. Cut each in half, through stem end.
Add olive oil, brussels sprouts, and cumin seeds to a 5- to 6-quart pan over high heat; stir often until sprouts are slightly browned, about 5 minutes. Add 1 cup water (and the basil if using dried); cover, reduce heat to medium-high, and cook, stirring occasionally, until sprouts are tender when pierced, 6 to 8 minutes. If liquid evaporates before sprouts are tender, add a little more water to prevent scorching.
Uncover and add butter; stir often until butter is melted. Stir in fresh basil, if using, and salt and pepper to taste. Pour into a serving bowl.