In a large skillet, heat oil over medium heat. Add onion, carrot and celery; cook and stir until tender, 4-5 minutes. Add garlic; cook 1 minute longer. Transfer to a 5-qt. slow cooker. Add the next 7 ingredients. Cook, covered, on low 5-6 hours, until sweet potatoes are tender., Stir in salmon, milk and parsley. Cook, covered, 30-40 minutes longer, until fish just begins to flake easily with a fork.