Combine brown sugar, chili powder, salt, onion powder and allspice in medium bowl. Set aside half the spice mixture (about 1/3 cup.); sprinkle the rest over both sides of ribs. Pour 1/2 cup root beer into slow cooker and add ribs. Cover and cook on low 5-6 hours or on high for 3 1/2-4 hours, until ribs are very tender.
With 10 minutes left on ribs, combine remaining root beer and reserved spice mixture in medium saucepan over medium-high heat. Bring to boil, stirring to dissolve sugar. Add cornstarch mixture and stir until sauce thickens, just a few seconds. Remove from heat; set aside.
Remove ribs to platter and cover. Strain the cooking liquid and pour off fat. Add 1/3 cup remaining liquid to sauce; stir until smooth.
Brush ribs with sauce, serve with remaining sauce on side.