Melt butter in large saucepan over medium heat. Cook onion, carrot, celery, garlic, salt and pepper for 3 to 5 minutes or until softened. Stir in Brussels sprouts and thyme; cook for 3 to 5 minutes or until well coated and start to soften. Sprinkle with flour; cook for 2 minutes. Gradually stir in broth. Bring to a boil.
Stir in corned beef, potatoes, cream and bay leaves. Reduce heat to medium-low. Cook for 15 to 18 minutes or until potatoes are tender. Stir in corn and chives. Remove bay leaves before serving.
• Serve with saltine crackers.
While trimming the Brussels sprouts, reserve some of the outer leaves. Blanch them in boiling water for 1 minute and use as a garnish for the soup.