Preheat the oven to 325 degrees . Spread the walnuts on a baking sheet and roast until well toasted and fragrant, 10 to 12 minutes.
In a large saucepan with a tight-fitting lid, melt the butter over medium heat. Add the rice and toast for a minute or two. Add 2 cups chicken stock and bring to a boil, then lower the heat, cover and simmer for 10 minutes. Add the apple and simmer for 8 minutes.
While the rice cooks, using a food processor, pulse 1/4 cup chicken stock, the parsley, dill and 1/4 teaspoon salt until finely chopped. Stir into the rice during the last minute of cooking. Turn off the heat and let the rice stand, covered, for 1 to 2 minutes before fluffing with a fork. Transfer to a serving dish and stir in the cheese.
Meanwhile, in a large skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Pat the chicken dry and season liberally with salt and black pepper. Add to the skillet and cook, turning once, until browned, about 10 minutes. Transfer the chicken to a platter. Drain off all but 1 tablespoon of the fat in the skillet and add the vinegar. Cook, scraping up the pan drippings, then add the remaining 1/4 cup chicken stock, the maple syrup and black pepper to taste. Cook until thickened, about 1 minute. Add the chicken and walnuts and spoon with the sauce. Loosely cover the pan with foil and simmer for 5 minutes. Serve the chicken, sauce and nuts with the rice alongside.