Add water, bouillon, onion, celery, chicken, ham, tarragon, basil and garlic powder to slow cooker. Cover and cook on LOW for 4-6 hours. Remove chicken and shred. Then add back into the slow cooker.
Prepare a roux. Melt butter over low heat in a skillet and add flour very slowly while whisking it in to the butter. Slowly stir in 1 cup hot soup. Stir until thickened. Then add in another 2 cups of soup and stir until smooth. Add all back into the slow cooker and stir. Season to taste.
Ladle soup into individual serving bowls and top with shredded Swiss cheese.