Bring broth to a boil over high heat; boil about 20 minutes, until mixture is reduced to 1/2 cup.
Process broth, sugar, and next 4 ingredients in a blender until smooth, stopping to scrape down sides. Turn blender on high; gradually add oil in a slow, steady stream. Add salt, pepper, and bourbon.
*Note: Walnut vinegar can be found at Williams Sonoma.