In a large pot, heat a little oil over medium heat. Add the chopped onion and garlic, and sauté until translucent, about 5 minutes.

Add the diced zucchini, potato, and corn. Stir and cook for another 5 minutes.

Pour in the vegetable broth and bring to a boil. Reduce heat and let simmer for 20 minutes, or until the potatoes are tender.

Use a blender to puree half of the chowder for a creamy texture, then return it to the pot.

Stir in the milk, thyme, salt, and pepper. Heat through for another 5 minutes.

Serve hot, garnished with fresh parsley and cheese if desired.