Add carrots, potatoes, broccoli, onion, garlic, vegetable broth, thyme, rosemary, salt, and pepper to the slow cooker.
Cover and cook on low for 5 hours or until all vegetables are tender.
Use an immersion blender to partially blend the soup, leaving some chunks for texture, or transfer half the soup to a blender and puree before returning to the pot.
Stir in evaporated milk and cream cheese cubes until the cream cheese is fully melted and incorporated.
Add shredded cheddar cheese and stir until melted and creamy.
Taste and adjust seasonings, then serve hot with fresh herbs or crusty bread if desired.