Preheat the oven to 400 degrees F. Spray a 13 by 9-inch baking dish with cooking spray.
For the sauce: In a 2-quart saucepan, melt the butter over medium heat. Add the flour and whisk until smooth. Gradually add the warm milk, whisking constantly to prevent lumps. Simmer over medium heat, whisking constantly, until the sauce is thick and smooth, about 8 minutes (do not allow the mixture to boil). Remove from the heat and season with salt and pepper, to taste.
For the farro: In a large bowl, add the cheeses and stir to combine. Remove 1/2 cup of the mixture and reserve. In a large stock pot, add the chicken broth and bring to a boil over medium-high heat. Add the farro, reduce heat and simmer, stirring occasionally, until the faro is tender, about 25 minutes. Drain, if necessary. Add the farro, thyme, and sauce to the bowl with the cheese. Stir until combined and season with salt and pepper, to taste. Pour the mixture into the prepared baking dish and top with the reserved 1/2 cup of cheese. Sprinkle the top with bread crumbs and drizzle with olive oil.
Bake until the top is golden brown and forms a crust, about 25 to 30 minutes. Remove from oven and let stand for 5 minutes before serving.