Special equipment: 1 (3-inch) 9-inch springform pan; a 10 by 15-inch jelly-roll pan
Position a rack in the middle of the oven and preheat to 350 degrees F. Butter the bottom of the springform pan and line with parchment or waxed paper. Set aside.
To make the base: Beat together the butter and sugar by hand until light and fluffy. Beat in the yolk until smooth. Combine the flour, baking powder, and salt. With a rubber spatula, gently fold into the butter mixture. The mixture will be crumbly.
Transfer the dough into the prepared springform pan and use your hands to pat it down evenly and firmly over the bottom. Bake for about 25 minutes, until the crust is golden and baked through. Transfer to a rack and cool base completely.
To make the filling: Combine the rum and lemon juice in a medium, heatproof bowl, and sprinkle the gelatin over the surface. Allow to soak for 5 minutes, then place the bowl over a small pan of gently simmering water and stir several times to melt the gelatin, about 1 minute. Remove the bowl from the pan and cool the gelatin slightly.
In the bowl of a heavy-duty mixer fitted with the paddle attachment, beat the cream cheese at medium speed until soft and light, scraping the bowl and beaters often. Beat in the cream until smooth. Combine the egg whites and sugar in the clean, dry bowl of the electric mixer and heat over simmering water, whisking constantly, until the egg whites are hot and sugar is dissolved. Attach the bowl to the mixer and whip with the whisk attachment at medium speed until cold and firm. Beat 1/4 of the cream cheese mixture into the dissolved gelatin, then beat the gelatin mixture into the remaining cream cheese. Fold in the meringue in several additions. Pour the filling into the prepared pan and refrigerate until at least 6 hours or overnight.
To prepare the almonds: Position the rack in the middle of the oven and preheat to 325 degrees F.
Put the almonds in a jellyroll pan, pour the egg whites over them, and rub the almonds between the palms of your hands to coat evenly. Stir in the sugar. Bake for about 20 minutes, stirring often, until the almonds are well toasted and sugar has caramelized slightly. Cool, and store in a tin or jar at room temperature until ready to use.
To make the glaze: Combine the water and lemon juice in a small bowl and sprinkle the gelatin over the surface. Allow to soak for 5 minutes.
Bring the jelly to a boil and add the gelatin mixture. Return to a boil, and remove from heat. Add the food coloring and pour over the chilled cheesecake. Chill again to set the glaze.
To unmold the cheesecake, run a knife or thin spatula around the inside of the pan pressing the knife against the pan, not the cake. Unbuckle the pan side and lift off. Leave the cake on the base, or run a spatula under the cake base and slide the cake onto a platter. Press the sugared almonds around the sides.
Keep refrigerated until time to serve. To serve, cut the cake into wedges with a knife warmed in hot water and wiped dry, refrigerate leftovers.