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Make and freeze the stuffing: Mash together the goat cheese, shredded cheese, cranberries, Italian seasoning and salt and pepper to taste in a bowl with a fork. (You can use your hands to mix it really well.) Taste a 'lil bit and add a pinch of salt if needed. Divide the cheese mixture into four sections and shape into torpedo-like logs a bit shorter than the length of the chicken breasts. Wrap each in plastic wrap. Freeze until firm, at least 1 hour or up to overnight.
Prepare the chicken: Use a paring knife to cut a pocket into the short, fat end of a chicken breast, that will run through much of the length of the breast, without cutting all the way through. It may take a few strokes with the knife. Repeat with the remaining chicken breasts. Remove the stuffing from the freezer and insert one log in each pocket. If necessary, trim the logs to fit into the pockets. Secure the openings with toothpicks.
Season and grill the chicken: Preheat the grill for direct and indirect grilling at 350 degrees F and oil the grates.
Brush olive oil on the chicken and sprinkle on all sides with salt and pepper. Place the chicken over the direct heat of the grill and cook until a peek beneath reveals grill marks, 5 to 7 minutes. Flip and place over the indirect heat of the grill to finish. Remove when a check with a thermometer shows the chicken to be at around 155 degrees F, 20 to 25 minutes. Remove the chicken from the grill and tent with aluminum foil for 5 to 10 minutes. The temperature of the chicken should increase to 165 degrees F.
Make the glaze: Combine the chicken stock, cranberries, honey, Italian seasoning and salt and pepper to taste in a small saucepan over medium-high heat. Cook, stirring, until reduced and slightly thickened, about 15 minutes.
Remove the toothpicks from the chicken, transfer to plates, and serve each with a spoon of glaze over the top.