To make the almond cream: Cream butter and sugar until light and fluffy. Add egg, almond flour, rum, vanilla, flour, and salt. Beat until creamy. Can be refrigerated for up to 1 week.
To poach the pears: Peel pears and cut in half. Use a grapefruit spoon or melon baller to seed and core. In a large pot, have water, sugar and spices at a simmer. Add pear halves and simmer for about 10 minutes, or until soft, but still holding their shape. Remove from heat and store in cooking liquid until ready to use.
Unfold 1 sheet of puff pastry on a floured surface. Use your tart pan to cut out a circle. Remove excess puff pastry and roll out so it is about 2 inches larger. Place in tart pan, carefully pressing edges into fluted sides of pan.
Repeat with second piece of pastry.
Dock bottom by piercing with a fork all over. Freeze for about 10 minutes.
Bake in a 350 degree oven until light brown, about 10 minutes. Remove from oven and allow to cool.
In the meantime, cut pears into about 1/8-inch slice. You can leave the halves whole or break apart. I like to leave whole and use a spatula to transfer to the tart.
Fill each tart with half of the almond cream. Top with pears. Sprinkle each tart with half of the sliced almonds. Cover with foil. Bake at 350 degrees for about 45 minutes. Remove foil and bake for another 10 minutes. Remove from oven to cool on a rack.
Heat almond preserves until liquid enough to brush on the tops of the tarts.