Heat olive oil in a large pot over medium heat.
Add zucchini, onion, basil, and salt. Saute, stirring often, until vegetables start to soften, about 10 minutes.
Add vegetable stock. Partially cover the pot and simmer for 20 minutes. Uncover and let cool.
Transfer to a blender and puree in batches, or use an immersion blender, until soup is very smooth. Stir in kefir and puree again. Taste and add salt and pepper if desired.
Ladle into a bowl. Top with tomato strips for garnish if desired.