Heat the olive oil in a pot over medium heat; cook and stir the potatoes and carrots in the hot oil until hot, about 10 minutes. Season with salt, garlic powder and onion powder. Add the chicken stock; continue cooking until the potatoes and carrots are soft, 10 to 15 minutes more.
Puree about half of the potato-and-carrot mixture in a blender. Return the pureed soup to the pot. Stir the cheddar cheese into the soup until melted. Ladle the soup into bowls and garnish with parsley to serve.