Heat a large saucepan over medium heat, add the olive oil and heat through. Add the celery, carrots and onions and sauté until the onion is tender, about 5 minutes.
Add the flour and stir to combine. Let the roux cook, stirring constantly, for 1 minute until it’s a pale golden brown.
Add the stock, stirring to combine. Season to taste with salt then add the rice. Simmer the soup on medium-low heat until the rice is tender and some of the grains have burst open, about 30 minutes.
Stir in the shredded turkey and kale, simmering for an additional 10 minutes, until the kale has wilted. Stir in the heavy cream.
For the garlic oil:
Add the vegetable oil to a small saucepan and heat over medium-low heat. Add the sliced garlic and fry, stirring occasionally until the garlic is crisp, about 5 minutes.
For serving:
Ladle the soup into bowls and drizzle with the garlic oil just before serving.