In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced zucchinis and corn kernels to the pot. Cook for about 5 minutes, stirring occasionally, until the zucchinis begin to soften.
Pour in the vegetable broth and bring to a boil. Reduce the heat and let it simmer for 15 minutes.
Using an immersion blender, blend the chowder until smooth, leaving some chunks for texture.
Stir in the heavy cream, salt, black pepper, smoked paprika, and cayenne pepper (if using). Simmer for another 5 minutes to heat through.
Remove from heat and stir in the fresh basil and lime juice. Adjust seasoning if necessary.
Serve hot, garnished with additional basil if desired.