1. Preheat oven to 425°.
2. Combine first 5 ingredients in a large bowl; add 2 tablespoons oil, 3/8 teaspoon salt, and 1/4 teaspoon pepper. Toss well to coat; arrange in a single layer on a large jelly-roll pan. Bake at 425° for 40 minutes or until vegetables are browned and tender, stirring every 10 minutes. Remove from oven; cool to room temperature.
3. Combine remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, vinegar, mustard, honey, and garlic in a large bowl, stirring with a whisk. Gradually add the remaining 3 tablespoons oil, stirring constantly with a whisk. Add roasted vegetables; toss to coat. Sprinkle with parsley.
Make-ahead tip: Roast the veggies several hours ahead; toss with vinaigrette about an hour before the party. Serve at room temperature.