In a medium-sized bowl, mix together the mustard, honey and red wine vinegar. While whisking, slowly drizzle in the EVOO until the dressing thickens. Season with salt and freshly ground black pepper. Toss the coleslaw and the radishes with the dressing and let sit while you prepare the burgers.
In a small saucepan, cook the apples, cider vinegar, brown sugar and nutmeg until the apples are soft, about 10-15 minutes. Once the mixture has reduced and is thickened, add in the cranberry sauce and raisins. Allow to sit while you make the burgers.
In a large bowl, combine the ham, cheese, chicken, thyme, grill seasoning and season with salt and freshly ground black pepper. Once mixed together, flatten the meat in the bottom of the bowl and score into 4 equal triangles. Form patties about 1-inch thick. Preheat a large non-stick skillet with 2 turns of the pan of EVOO, about 2 tablespoons. Add the patties and cook for 5-6 minutes on each side, or until cooked through.
Place each burger on a toasted English muffin, top with some of the apple-cranberry chutney and serve with honey-Dijon slaw and salt and vinegar potato chips alongside.