01 - Heat olive oil in a large heavy-bottomed pot over medium heat. Add the diced onion, carrots, and celery. Sauté for 5 minutes, stirring occasionally, until the vegetables have softened and the onions turn translucent.
02 - Stir in the minced garlic and cook for 1 minute, stirring constantly, until fragrant and lightly golden.
03 - Add the corn kernels, diced zucchini, and chopped potatoes to the pot. Season with salt, black pepper, smoked paprika, and dried thyme. Cook for 5 minutes, stirring occasionally, to allow the seasonings to coat the vegetables evenly.
04 - Pour in the vegetable broth and bring the mixture to a gentle boil. Reduce the heat to low, cover the pot, and simmer for 15 minutes, or until the potatoes are fork-tender.
05 - Using an immersion blender, blend a portion of the chowder directly in the pot until partially smooth, leaving some vegetables intact for a hearty, chunky texture. Alternatively, transfer about 2 cups of the chowder to a standard blender, puree until smooth, and return it to the pot.
06 - Stir in the milk and heat gently over low heat for 2 to 3 minutes until warmed through. Do not boil.
07 - Taste and adjust the seasoning with additional salt and pepper if needed. Ladle into warm bowls and garnish with fresh chives, parsley, and shredded Parmesan or vegan cheese if desired. Serve immediately.