Pour the oil into a large pot over medium-high heat. Add the farro and toast for 1 minute. Season with salt and pepper.
Add the stock and bring to a boil. Reduce heat to medium and simmer about 20 minutes.
While the farro simmers, melt the butter in a large saucepan over medium-high heat.
Add the onion, celery, carrots, and garlic, season with salt and pepper, and saute 4 to 5 minutes until the vegetables turn translucent. Add the thyme and sage and saute 1 minute more.
Stir in the flour and cook about 2 minutes, stirring, to remove the raw flour flavor and any dry pockets.
Whisk in the milk until no lumps remain. Reduce heat to medium-low and simmer 3 to 4 minutes until it begins to thicken.
Once thick enough to coat the back of a spoon, stir the mixture into the farro and stock. Add the shredded chicken and season with salt and pepper.
Simmer 20 to 25 minutes until the soup thickens and the farro is cooked through. Adjust seasoning and serve.
