Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic, thyme, rosemary, and red pepper flakes (if using) and cook for 1 minute more, until fragrant.

Add potatoes and chicken broth to the pot. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until potatoes are tender.

Carefully transfer the soup to a blender or use an immersion blender to blend until smooth.

Return the soup to the pot. Stir in milk or half-and-half and cheddar cheese. Heat until cheese is melted and soup is heated through. Do not boil.

Stir in fresh parsley. Season with salt and pepper to taste.

Serve hot, topped with additional shredded cheddar cheese and fresh parsley, if desired.