Heat oil or butter in a large pot over medium heat.

Add the diced onion and cook until softened.

Stir in the minced garlic, carrots, and celery, and cook until they begin to soften.

Add the cubed potatoes and pour in the broth.

Season with salt, black pepper, thyme, and rosemary.

Bring the soup to a boil, then reduce heat and simmer until the potatoes are tender.

Stir in the cooked chicken and cook until heated through.

In a separate bowl, whisk together the Greek yogurt and milk until smooth.

Slowly add this mixture to the pot, stirring constantly to prevent curdling.

Simmer gently for a few more minutes until the soup is creamy and well combined.

Adjust seasonings to taste and ladle into bowls.

Garnish with fresh parsley or optional cheese before serving.