Preheat an oven to 350 degrees. Spread the walnuts on a baking sheet and toast in the oven until lightly browned and fragrant, about 7 minutes. Remove from the oven and let cool. Working from the stem end, use a melon baller to remove the core from each apple, scooping out the stem and seeds making a deep hole for filling: work to within about 1/2-inch of the bottom of the apple. (Alternatively, remove the core with an apple corer and widen the hole with a small spoon.) Peel the skin from the top half of each apple. In a small bowl, blend together the brown sugar, butter, and cinnamon. Mix in the walnuts. Spoon equal amounts of the filling into the centers of the apples. Set the filled apples in an 8-inch square baking pan or other baking pan just large enough to hold them snugly. In a small pan over medium heat, warm the honey with apple juice, stirring until the honey dissolves. Pour around the apples. Spoon some of the liquid over the sides of the apples to moisten them, but do not spoon over the tops. Bake, basting the sides once or twice with the pan juices, until the apples are tender when pierced, about 40 minutes. Remove from the oven, let cool, and serve in bowls with the pan juices spooned over the tops.