Spray 6- to 7-quart slow cooker with cooking spray. In 12-inch nonstick skillet, heat oil over medium-high heat. Cook onions and garlic in oil 4 to 5 minutes, stirring occasionally, until softened. Add cabbage; cook 2 to 3 minutes until slightly wilted. Spoon mixture into slow cooker.
Add potatoes, broth, water, bay leaves, 1/3 cup parsley and the pepper to slow cooker; stir. Top with corned beef; sprinkle with contents of spice packet. Cover; cook on Low heat setting 6 hours.
In small bowl, stir together horseradish sauce ingredients. Refrigerate until serving time.
Remove beef from slow cooker. Discard bay leaves. Chop beef, discarding fat. Return beef to slow cooker; stir. Serve with horseradish sauce.