For the caramel, stir the sugar and 2 tablespoons water together in a medium skillet. Cook over medium heat, stirring occasionally, until the sugar is melted and the syrup is boiling. Once it boils, don’t stir, just swirl occasionally so the caramel cooks evenly. Simmer until the syrup begins to turn a medium amber color, about 7 to 8 minutes. Pour the caramel immediately into a 10-inch round heatproof pie dish or shallow casserole.

Preheat oven to 325 degrees. Choose a roasting pan large enough to hold the pie plate, and place it on the center rack of the oven. Heat a kettle of water to boiling.

Put the crumbled cookies in a blender, and blend in bursts until finely ground. Pour in the cocoa and sugar, and pulse to mix with the cookies. Pour in the milk, eggs, yolk, rum, and baking powder, and blend at low speed, stopping occasionally to scrape down the sides of the jar, until smooth. Pour in the heavy cream, and blend just enough to incorporate it. Scrape into a mixing bowl and stir in the pears.

Pour the chocolate-pear mixture into the prepared dish, and set the dish in the roasting pan. Pour in enough of the boiling water from the kettle to come halfway up the side of the pie plate. Bake until firm in the center and lightly browned on top, about 40 minutes.

Remove from the oven, and let cool in the water bath until you can safely remove it. Cool on a rack to room temperature, then refrigerate until chilled. To serve, run a thin knife around the edge of the custard to loosen. Invert a plate large enough to hold the tart comfortably, then, in one quick motion, flip the tart over and set the plate down. The tart may take several seconds to work itself loose from the dish. After it does so, gently lift off the dish, and serve the tart cut into wedges.