In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the chopped zucchinis and diced potato. Cook for about 5 minutes, stirring occasionally.
Pour in the vegetable broth and add the dried thyme. Bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes, or until the vegetables are tender.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, you can transfer the soup in batches to a blender.
If using, stir in the heavy cream for a richer flavor and season with salt and pepper to taste.
Serve hot, garnished with fresh basil if desired.