Combine 1/2 quart turkey broth, onion, celery, and carrot in a large saucepan; bring to a boil. Reduce heat; cover and simmer until vegetables are tender. Remove from heat; reserve vegetables and broth.
Melt butter in a small Dutch oven over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add remaining 1 quart turkey broth; cook over medium heat, stirring constantly, until thickened and bubbly. Gradually stir in warm half-and-half, salt, and pepper. Add reserved vegetables and broth, turkey, and rice. Cook over medium heat until thoroughly heated. Ladle into individual soup bowls; serve warm.