Place the slightly cooked vegetables in the slow cooker. Add the chicken broth, chicken, wild rice blend, and the seasoning packet from the Rice-A-Roni package. Cook on LOW for 7-8 hours or on HIGH for 3-4 hours.
Carefully remove chicken and shred the chicken with two forks.
In a sauce pan, melt the butter. Whisk flour into the butter. While whisking, slowly pour in half-and-half. Cook mixture until it thickens, approximately 5-6 minutes, whisking at it cooks.
Add milk mixture, the shredded chicken, and the cooking wine to the slow cooker. Mix together.