Fill a large bowl with ice water; set aside. Place a steamer basket in a large saucepan with a lid; fill with 1 inch of water. Bring to a boil; add sprouts, cover, and cook until easily pierced with the tip of a paring knife, 10 to 15 minutes (depending on size).
In a small bowl or liquid-measuring cup, combine mustard, vinegar, and oil. Season with salt and pepper, and whisk until combined.
Lift basket and transfer sprouts to ice water. Let stand until cooled, about 5 minutes. Drain well and pat dry; cut lengthwise through core into quarters. Serve sprouts drizzled with vinaigrette.
To make ahead: Trim, steam, cool, and quarter brussels sprouts up to 1 day ahead; refrigerate in a resealable plastic bag lined with a paper towel. Make vinaigrette up to 1 day ahead; cover, and refrigerate separately from sprouts. Serve sprouts drizzled with vinaigrette.