Wash and dice the zucchinis, and dice the onion. If using fresh corn, remove the kernels from the cob.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and minced garlic, cooking until the onion becomes translucent (about 3-4 minutes).
Add the diced zucchini to the pot and cook for an additional 3-4 minutes, stirring occasionally.
Stir in the corn kernels, vegetable broth, salt, black pepper, and paprika. Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes, until the zucchini is tender.
If you prefer a smoother texture, use a blender or an immersion blender to purée part of the chowder, leaving some chunks for texture.
Return the pot to low heat and stir in the heavy cream, stirring until well combined. Allow it to heat through for an additional 2-3 minutes. Adjust seasoning to taste.
Serve hot, garnished with fresh parsley if desired.