Heat olive oil in a large saucepan over medium heat. Add the carrot, onion and celery and sauté until soft (about 5-10 minutes).
Add the garlic and thyme, then season with salt and pepper.
Add the zucchini, sautee for a few more minutes. Add the broth and let the soup simmer for about 15 minutes.
Puree the soup with an immersion blender (or in a regular blender) until smooth.
Turn the heat to low, add the cheese and milk and stir until melted (about 5 minutes)