Heat the oil in a pot over medium heat. Add the onion, garlic, carrots and thyme and cook until the vegetables are softened, about 5 minutes. Mix in the flour until well combined. While stirring, slowly pour in the stock and bring to a simmer. Add the potatoes and cook until the vegetables are quite tender, about 20 minutes. Purée the soup in a food processor or blender. Return the soup to the pot and bring it back to a simmer. Stir in the milk and season with salt and pepper. Pour into bowls, top with cheese, garnish with parsley, and serve.