In a pot with olive oil and butter, soften the onion cut into small cubes (stirring occasionally, on medium heat, about 5 minutes).
Add peeled and diced potatoes and stir. Sauté together for about 2-3 minutes, stirring occasionally.
Add grated garlic, pour in broth and bring to a boil. Meanwhile, add turmeric, pepper and salt to taste if needed.
After bringing to a boil, cook the soup for about 2-3 minutes, then add zucchini cut into cubes (somewhat larger than the potatoes). Cook for about 8-10 minutes.
Remove from heat, add dill and cream. Serve with feta and bread.