In a large skillet over medium-high heat, saute onion, garlic, 1 tablespoon of the parsley, and carrots in the oil for 2 to 3 minutes or until onions are translucent. Remove from skillet and place in slow cooker. Add corned beef brisket and pickling spice to the slow cooker and add water. Cover and cook on low for 6 hours or until brisket is tender.