Heat oil over medium heat in a soup pot; add onion and cook,
stirring often, until softened, about 3 minutes.
Add broth and potato, increase heat to high and bring to
a boil. Reduce heat to medium-low and cook at a simmer,
stirring occasionally, until potato is fork tender, about 15
minutes. Stir in milk and cook a further minute.
Transfer half the soup to a blender and puree. Return to pot
and stir in turkey, rice, and cayenne. Cook over medium-low
heat, stirring often, until thick and piping hot, about 6 minutes.
Season with salt and pepper and serve immediately.