Preheat oven to 450°.
Cut parsnips crosswise into thirds, then lengthwise into quarters. Cut fennel bulbs in half vertically. Cut each half lengthwise into 1/2-inch-thick slices.
Place parsnips, fennel, sweet potato, and onion in a large roasting pan; drizzle with oil and vinegar. Sprinkle with salt, rosemary, thyme, and pepper; toss well to coat. Add 1/4 cup water to pan. Roast for 35 to 40 minutes, or just until vegetables are tender and beginning to brown (stir once halfway through cook time). Top with goat cheese before serving.