Start by setting a Dutch oven or a heavy-bottomed soup pot over medium heat. Add the butter and let it melt gently. Once melted, stir in the diced yellow onion. Sauté until the onion becomes soft and translucent, which should take about 5 minutes. Then, add in the minced garlic and cook for an additional minute until that delightful aroma fills your kitchen.
Next, it’s time to introduce all those lovely flavors! Add the chopped zucchini along with the dried rosemary, thyme, oregano, celery salt, salt, black pepper, and cayenne pepper if you're feeling adventurous. Stir everything together and allow it to cook for about 5 minutes.
Add in your diced russet potatoes, chicken broth (or vegetable broth if you prefer), and soy sauce to the pot. Give everything a good stir to combine all those ingredients nicely. Bring your soup to a boil, then reduce the heat to medium so it can simmer gently.
Cover your pot partially with a lid and let it simmer for about 15-20 minutes. You want both the zucchini and potatoes to be fork-tender.
Once your vegetables are tender, remove the pot from heat. Use an immersion blender (or transfer batches carefully to a regular blender) to puree your soup until it's completely smooth.
After blending, return the pot to low heat and stir in the heavy cream followed by the shredded cheddar cheese. Keep stirring until both are fully melted and combined into your soup.
Ladle your creamy zucchini soup into bowls while it's warm! It’s perfect on its own or paired with some crusty bread or a light salad for a complete meal.