In a large pot, warm the olive oil over medium heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes. Then, incorporate the minced garlic and cook for an additional minute.

Add zucchini, thyme, salt, and pepper. Cook for about 5 minutes, stirring, until zucchini softens.

Pour in the vegetable broth and bring to a boil. Reduce the heat to low, cover the pot, and let it simmer for 15 minutes, until the zucchini is tender.

Add the baby spinach and stir; let the spinach soften.

Remove the pot from heat. Use an immersion blender to blend the soup until smooth. Alternatively, carefully transfer the soup to a blender in batches and blend. If needed, add more broth to thin the soup after blending.

Stir in the Greek yogurt and half-and-half until well combined. Taste and adjust seasoning with salt and pepper if needed.

Serve hot, garnished with fresh basil leaves if desired.