Preheat the oven to 325°F/160°C, and place the cake ring on a baking sheet lined with parchment paper.
Mix all the ingredients for the crust, until combined, using a stand mixer with the paddle attachment, or simply a bowl with a rubber spatula. Press it down evenly with your hands into the cake ring, and bake for 20 minutes.Allow to cool down.
Once the crust is baked, prepare the almond cream by combining all the ingredients together in a bowl. Spread evenly on top of the crust, without going all the way to the edges.
Drain the pear halves and slice them thinly (you can also leave them uncut). Place them onto the almond cream, and sprinkle the tart with sliced almonds. Bake for 40 minutes at 325°F/160°C.
While the tart is baking, make the rum syrup: bring the water and the sugar to a boil in a small pot. When the sugar is completely dissolved, remove from the stove, and add the rum.
Brush the tart with the syrup, remove the ring, and allow to cool down.
Dust with powdered sugar right before serving.
Store in an airtight container for up to 5 days in the fridge, or 3 months in the freezer.