Heat olive oil or butter in a large pot over medium heat, add chicken, season lightly with salt and pepper, and cook until fully cooked through, then remove and shred.
In the same pot, add chopped onion and cook until soft, then stir in garlic and cook briefly until fragrant.
Pour in chicken broth and stir well, scraping the bottom of the pot to release flavor.
Lower the heat and add softened cream cheese, stirring until completely melted and smooth.
Slowly stir in heavy cream until the broth becomes rich and creamy.
Return shredded chicken to the pot and mix well.
Add shredded cheddar cheese, dried parsley, and dried thyme, stirring until the cheese melts fully.
Simmer gently for several minutes until slightly thickened, then adjust seasoning with salt and black pepper.
