Combine chicken, 1 cup water, garlic and bay leaf in large saucepan. Cover and simmer just until chicken is cooked through, turning once, about 15 minutes. Transfer chicken to plate; cool. Shred chicken. Pour cooking liquid into measuring cup, adding more water to measure 1 cup if necessary. Reserve cooking liquid.
Whisk flour and cornstarch in heavy large saucepan. Add 1 cup milk; whisk until smooth. Stir in 1 cup milk, tarragon, salt, nutmeg and reserved 1 cup chicken cooking liquid. Stir over medium heat until mixture thickens and boils, about 5 minutes. Add wine; stir until mixture is very thick, about 2 minutes longer. Remove from heat. Stir in shredded chicken and spinach. (Can be made 1 day ahead. Cover and chill. Rewarm over medium low heat, stirring frequently, before continuing.)