Place corned beef in large pot or Dutch oven and cover with water. Add the spice packet that came with the corned beef. Cover pot and bring to a boil, then reduce to a simmer. Simmer approximately 50 minutes per pound until tender. Remove meat and let rest 15 minutes. Slice meat across the grain.
Whisk together olive oil, balsamic vinegar, mustard, salt, and pepper in small bowl. Place the shredded cabbage in a large bowl and pour the dressing over it; toss to coat the cabbage with the dressing.
Spread a layer of mustard on 6 slices of toasted bread. Place some shredded cabbage and corned beef on each slice and top with remaining slices of bread.