Place currants in small bowl. Heat vinegar in saucepan over medium heat until hot (do not boil). Pour vinegar over currants; let soak until currants soften, 15 to 20 minutes.
Place cabbage in large bowl; set aside. Heat a splash of olive oil in a smalll nonstick skillet over medium- high heat. Add shallot and sauté 1 minute. Remove from heat. Stir in currant- vinegar mixture and olive oil. Season with salt and freshly ground black pepper.
Pour the mixture over cabbage and toss to coat. Season to taste with salt and pepper. Let stand 5 to 10 minutes. Add almonds and parsley; toss to blend.