Prep the vegetables by washing and chopping the broccoli, slicing the carrots, dicing the onion, and mincing the garlic.

In a large pot, heat olive oil over medium heat, then sauté onion and garlic for about 3-4 minutes.

Add carrots and broccoli, seasoning with salt, pepper, and thyme; cook for another 4-5 minutes.

Pour in vegetable broth and bring to a simmer; cook uncovered for 10-12 minutes until tender.

Blend the soup using an immersion blender for 30 seconds, keeping some texture.

Stir in milk and shredded cheese, mixing until smooth.

Add chopped kale or spinach, allowing to simmer for an additional 2-3 minutes.

Serve hot, garnished with extra cheese and black pepper if desired.