In a small bowl, stir together the chicken broth and arrowroot flour, making sure the flour is completely dissolved and there are no clumps. Set aside.
Combine the coconut milk, nutritional yeast, basil, and salt in a saucepan. Stir well. Bring to a boil over high heat, then reduce to low and stir in the broth-arrowroot mixture. Stir constantly until the sauce thickens, about 1 minute.