For the marinade: Place the red wine vinegar, apple cider vinegar, the mustards, and honey in a food processor. Turn it on and drizzle in the olive oil until fully incorporated (emulsified). Marinate the chicken breasts overnight in this mixture.
Preheat grill or grill pan on high. Remove chicken breasts from the marinade and transfer to a plate. Season them with salt and pepper. Mark the chicken breasts by grilling them only long enough to make grill marks and then rotating them about 45 degrees to make crosshatch marks. Do this on 1 side only. The chicken breasts should still be completely raw inside. Hold breasts in refrigerator until ready to stuff.
For the stuffing: Peel, core, and very roughly chop the apples. Melt the butter in a saute pan over medium/high heat and add the apples. Cook the apples for roughly 5 to 10 minutes or until they are deeply browned. Remove from heat and transfer to a mixing bowl. Add the fontina and cherries and mix. Season, to taste, with salt and pepper.
For the chicken: Preheat your oven to 400 degrees F. Cut a slit in the side of each breast (in the thicker part) about 1-inch wide, creating a pocket almost as large as the breast itself. Stuff the breasts with the apple stuffing mix cramming in as much as possible without ripping the breast. At this point the breasts are ready to bake and can either be held in the refrigerator for up to 24 hours or baked right away. When ready to bake, place on a baking sheet and bake for about 12 to 15 minutes or until an instant-read thermometer registers 155 degrees F in the thickest part of the breast.
Professional Recipe: This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe in the proportions indicated and therefore cannot make any representation as to the results.