Combine cauliflower, potatoes, beans, onion, garlic, broth, thyme, salt and pepper in a 6-quart slow cooker.
Cover and cook on low for 6 to 7 hours until cauliflower and potatoes are very tender.
Turn off the cooker and let the soup stop bubbling for 5 minutes. Blend with an immersion blender until smooth, keeping the blade submerged.
Stir in mustard and let stand for 2 minutes so the flavor distributes.
Toast bread without butter. Divide soup among 6 bowls and sprinkle each with 2 teaspoons Parmesan.
Serve one whole-grain toast slice with each bowl.