Preheat the oven to 400 degrees F.

Cut the pineapple in 1/2 lengthwise, keeping the greens on top intact. With a knife, hollow out each 1/2, leaving a 1/2-inch shell intact. Cut away and discard the cores. Chop 1 cup of pulp into 1/2-inch dice, place in a medium bowl, and toss with the rum. Reserve the remaining pulp for another use.

Place the pineapple shells on a baking sheet and bake until dry, 8 to 10 minutes. Remove from the oven and let cool completely.

Add the softened ice cream to the diced rum-soaked pineapple and mix until well incorporated. Place in the freezer to harden slightly. Scoop the ice cream into 4 (1/2-inch) scoops and place 2 in the center of each pineapple shell. Place on a small baking sheet and freeze until very firm, at least 4 hours or overnight.

Preheat the oven to 450 degrees F.

In a large bowl, beat the egg whites until foamy. Add the cream of tartar and beat until soft peaks form. Beating constantly, gradually add the sugar, and continue to beat until glossy and stiff peaks form. Transfer to a pastry bag.

Remove the pineapple halves from the freezer. Pipe the meringue in small rounds to completely cover the ice cream and resemble the outside of a pineapple. (Alternatively, spread the meringue with an offset spatula or back of a spoon in a mound over the ice cream. Bake until golden brown, 5 to 6 minutes.

Remove from the oven and place 1 pineapple 1/2 on each of 2 plates. Drizzle with chocolate sauce and serve immediately.