Preheat the oven to 400 degrees F.
Slice off about 1/4-inch of the top of each apple. (The apple tops are perfect for snacking.) Scoop out the seeds and core of the apple with a melon-baller to make a pocket. Peel off about a 1/2-inch band of the apple's skin along the upper half of the apple with a vegetable peeler. Brush the peeled part and the interior of the apple with lemon juice.
In a small mixing bowl, combine the butter, lemon zest, and sugar. Add the currants and nuts. Place some of the butter mixture and a cinnamon stick in each of the apples. Place the apples in an ovenproof baking dish just large enough to hold the apples upright. Pour in the cider and rum, bake until the apple is tender, about 30 minutes. Baste the apples with the cider/rum mixture with a bulb baster, 2 or 3 times, during baking.
Serve warm or at room temperature with softly whipped cream or vanilla or cinnamon ice cream.
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