For dressing, in a screw-top jar combine vinegar, olive oil, champagne mustard, green onion, garlic, and freshly ground pepper. Cover and shake well. Refrigerate 4 hours or overnight to blend flavors.
In a steamer basket over boiling water, steam Brussels sprouts, covered, for 10 to 15 minutes or until crisp-tender. In a colander, run Brussels sprouts under cold running water to cool. Drain. Cut sprouts in half. Cover and chill.
In a large salad bowl place mixed greens, sweet pepper strips, cherry tomatoes, and Brussels sprouts. Shake dressing and drizzle over the salad; toss gently to coat. Makes 4 servings.