Place large pot on stovetop over medium heat. Add 1 tablespoon butter and heat, swirling and tilting pot occasionally to distribute butter across entire surface, until butter is melted.
Once butter is melted, add 1 medium yellow onion and stir to incorporate. Sauté chopped onions, stirring occasionally, 5 minutes or until softened.
Add 3 cloves garlic and stir to incorporate. Sauté garlic and onions, stirring occasionally, 2 minutes or until garlic is softened and fragrant.
Add 6 cups chopped zucchini, 1 teaspoon salt, and ¼ teaspoon freshly cracked black pepper to pot. Stir to incorporate into onions and garlic mixture. Sauté zucchini, stirring occasionally, 10 minutes or until softened.
Pour 1 ½ cups low-sodium vegetable broth into pot. Stir to incorporate, making sure to scrape up any browned bits of food that may have stuck to bottom of pot. Reduce heat under pot to low and simmer mixture 15 minutes, stirring frequently.
After 15 minutes, remove pot from heat. Let mixture cool slightly, then insert immersion blender into pot and purée ingredients together until fully combined into smooth, creamy mixture.
Taste soup and stir in additional salt or black pepper if desired. When satisfied with flavor, portion soup into serving bowls and serve immediately.