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.