Combine 1 cup water, peppercorns, and the next 6 ingredients (peppercorns through garlic) in a small saucepan; bring to a boil. Reduce heat, and simmer 5 minutes. Remove from heat. Pour into a large bowl; cool to room temperature. Add remaining 6 cups water, salt, and sugar, stirring until salt and sugar dissolve. Pour salt mixture into a 2-gallon zip-top plastic bag. Add ice and brisket; seal. Refrigerate 3 days, turning bag occasionally. Remove brisket from bag, and discard brine. Pat brisket dry with paper towels.
Place brisket in a large stockpot; cover with water. Bring to a boil; skim foam from surface. Cover, reduce heat, and simmer 2 1/2 to 3 hours or until brisket is tender. Remove brisket from pan; keep warm. Reserve cooking liquid. Add carrots, cabbage, potatoes, and onions to reserved cooking liquid; bring to a boil. Reduce heat, and simmer 30 minutes or until tender.