In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the sliced zucchinis and diced potato to the pot, stirring to combine. Cook for about 5 minutes, allowing the vegetables to soften slightly.
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 carefully transfer the soup to a blender in batches.
Return the soup to low heat and stir in the heavy cream. Season with salt and pepper to taste. Heat through, but do not boil.
Serve hot, garnished with fresh basil leaves.