Note: If you prefer a thinner syrup, simply reduce the accumulated juices from the apple cooking bags for a few minutes in a small saucepan over high heat and add a tablespoon of Calvados or apple brandy at the end. Sally preferred the thicker version, whereas her husband preferred the thinner syrup!
At least 3 to 3.5 hours before serving
Preheat the water bath to 183°F (84°C).
Wash the apples and pat dry. If the apples have an uneven bottom and you want to present them "standing," use a small paring knife to trim a slice off the base of each apple so that it will sit upright. (They may already be flat enough to stand without trimming.) With the same knife or an apple corer and working from the base of the apple, carefully remove as much of the core (perhaps halfway up the inside of the apple) as you like, without removing so much that the apple can't hold its shape. Or you can leave the core in if you like.
Prepare three vacuum bags large enough to hold 2 apples each. Brush the inside of each bag with about a tablespoon of melted butter, going 3 to 4 inches up the side. Dust the inside of the bags with about half the superfine sugar. Place the open bags in the refrigerator or freezer for a minute or two to harden the melted butter.
Brush the prepared apples all over with the remaining melted butter. Place the coated apples and the remaining half of the superfine sugar in a large plastic bag and shake to cover the apples evenly with the sugar.
Remove the vacuum bags from the refrigerator, place two buttered-and-sugared apples in each bag, and vacuum seal.
Cook for 2 1/2 to 3 hours. The apples are buoyant and you will need to be sure that they are completely submerged by weighting them with a rack or something heavy enough to keep them from floating.
To prepare the optional nut garnish, toast the pistachios and almonds in a saute pan or in the oven until light golden brown and then sprinkle with the confectioners' sugar. Transfer to a strainer to remove any excess sugar. They should be lightly dusted with sugar. Set aside.
To make the optional syrup, stir together the superfine sugar and water in a small saucepan. Heat over high heat until the sugar has dissolved and the liquid begins to bubble all over. (In essence, you are creating a caramel.) Do not move or stir the contents. Watch the pan closely to be sure the mixture does not burn. The liquid will begin to turn a light amber color and once it has all turned an amber color, remove the pan from the flame and carefully add the apple juice. The liquid may want to bubble up in the pan, so have a lid ready to cover the pan once the apple juice has been added. Stir the contents of the pan and return to the burner on medium to medium-high heat. Add the arrowroot-water mixture to the pan, stirring constantly. Boil the ingredients until thickened, remove from heat, and add the Calvados or brandy. The final sauce will be more like a thick syrup than a caramel. Set aside until ready to serve the apples.
Remove the apples from the water oven and transfer them to a serving platter or individual plates. Serve as is, or drizzle with the syrup and sprinkle with the nuts. Top with ice cream, a dollop of whipped cream, creme fraiche, or plain Greek yogurt if desired. They are delicious hot or cold or at room temperature. They are extremely versatile!