Set a large, heavy pot over medium heat. Add the butter and tilt the pot to coat the bottom. Once the butter melts, add the chopped onion. Sauté for about five minutes, stirring now and then, until the onion is soft.

Stir in the minced garlic and cook for about two minutes until fragrant. Keep it moving in the pot so it does not burn. If the garlic starts to darken, lower the heat.

Add the chopped zucchini, salt, and black pepper. Sauté for about ten minutes, stirring now and then, until the zucchini softens.

Pour in the broth and scrape up any browned bits from the bottom of the pot. Turn the heat to low and simmer for 15 minutes, stirring often, until the zucchini is very tender.

Take the pot off the heat and let it cool slightly. Use an immersion blender to blend the soup until smooth and creamy.

Taste the soup and adjust the salt and pepper as needed. For a richer finish, stir in 2 to 4 tablespoons of room-temperature full-fat coconut milk or heavy cream before blending. Serve the soup right away while warm.