Saute the veggies. Melt butter in a 4 qt dutch oven and saute the onion, carrot, celery, and garlic until soft. Add the dijon and cook for 1-2 minutes. Sprinkle the flour over the top and stir it in. Cook the flour for 3-4 minutes, stirring often, to remove any raw flour taste.
Add the liquid. Stir in the white wine, if using, and the chicken broth. Make sure to stir well as you add the liquid so that there aren't any lumps. Bring to a gentle simmer. Simmer for 5 minutes or so, until thickened.
Add the ham and potatoes. Add the diced potatoes, bay leaves, and ham and simmer, covered, until the potatoes are very tender. Use a fork to gently smash some of them so that they thicken the soup a bit. Add the cream and simmer for another 5 minutes.
Season and add herbs. Season the soup to taste with salt and lots of freshly cracked pepper. Stir in the chopped dill and chives and any additional leftover veggies that you want to add. Serve Creamy Ham and Potato Soup with crusty bread for dipping.