Using a sharp knife, carefully slice goat cheese in 1/2"-thick slices. Place cheese in an 11" x 7" dish or other serving platter. Drizzle with oil. Combine honey and pepper; drizzle over cheese. Sprinkle with 1 tsp. thyme leaves. Cover and chill up to 2 days.
Remove cheese from refrigerator 1 hour before serving. Just before serving, drizzle a little vinegar over cheese. Garnish, if desired. Serve with lahvosh or other specialty cracker bread.
*Find fig balsamic vinegar at Williams-Sonoma or other cook stores.