In a large soup pot, melt the butter over medium heat. Add the diced onion and cook for about 5 minutes until it softens. Toss in the minced garlic, zucchini chunks, and the blend of seasonings. Stir occasionally and cook for another 5 minutes.

While the zucchini cooks, peel, rinse, and chop the potatoes into small, even pieces for quicker cooking.

Pour in the chicken broth and soy sauce, then add the chopped potatoes. Bring the mixture to a boil, then lower the heat to a gentle simmer. Skim off any foam that forms on the surface if needed. Let the soup simmer, partially covered, for around 20 minutes until the vegetables are tender.

Take the pot off the heat. Use an immersion blender to puree the soup, or transfer it in batches to a blender until smooth.

Return the pureed soup to low heat. Gently stir in the half-and-half.

Slowly sprinkle in the shredded cheddar cheese, stirring until fully melted and well combined. Remove from heat and serve hot!