Heat a large pot over medium-high heat and add olive oil.

Add diced zucchini, onion, and minced garlic; sauté for 5–7 minutes until onions are translucent.

Pour in the chicken broth, stir, and bring to a boil. Reduce heat to medium-low and cover; simmer for 20 minutes.

Remove from heat and cool for 10–20 minutes. Transfer to the refrigerator and chill for at least 1 hour.

Use an immersion blender to puree the soup until smooth. Stir in the sour cream and blend again until well combined.

Serve in bowls with a drizzle of olive oil, grated cheese, and fresh herbs, adding salt and pepper to taste.