Heat the olive oil in a large pot, then cook the onion and celery for about 5 minutes.
Stir in the garlic, smoked paprika, and thyme, cooking briefly until fragrant.
Add the potato, corn, zucchini, vegetable broth, salt, and black pepper.
Bring the soup to a boil, reduce the heat, and simmer for 18 to 20 minutes until the potato is tender.
Transfer about 2 cups of soup to a blender, blend until smooth, and return it carefully to the pot.
Stir in the low-fat milk and warm the chowder gently for another 3 minutes without boiling.
Add the parsley, taste the seasoning, and serve warm.