Make sauce Heat oil in heavy large pot over medium-low heat. Add green onions, white onions and garlic and sauté until tender, about 15 minutes. Mix in all remaining ingredients, adding bourbon last. Simmer sauce until thick and reduced to 7 cups, stirring occasionally, about 1 hour. Season to taste with salt and pepper. (Sauce can be prepared 2 weeks ahead. Cover and refrigerate.)
Make spice rub and ribs Mix first 7 ingredients in medium bowl. Rub spice mixture over both sides of rib racks. Arrange ribs on large baking sheet. Cover and refrigerate overnight.
Prepare barbecue (medium heat). Cut rib racks into 4- to 6-rib sections. Arrange ribs on barbecue. Grill until meat is tender, occasionally turning ribs with tongs, about 40 minutes. Using tongs, transfer ribs to work surface.
Cut rib sections between bones into individual ribs. Arrange on clean baking sheet. Transfer 3 cups sauce to small bowl; place remaining sauce in small saucepan and reserve. Brush ribs with sauce from bowl.
Return ribs to barbecue. Place pan of reserved sauce at edge of barbecue to rewarm. Grill ribs until brown and crisp on edges, brushing with more sauce from bowl and turning occasionally, about 10 minutes. Serve ribs with warm sauce.