Begin by bringing a saucepan of water to a gentle simmer. Add sugar and stir until dissolved, then carefully place the peeled, halved pears into the liquid. Allow them to poach for about 15-20 minutes until tender.

In a large mixing bowl, combine sugar, flour, cardamom, and cinnamon. Make a well in the center and add eggs and vanilla extract. Beat the mixture on medium speed for about 3-5 minutes until light and fluffy.

Preheat your oven to 350°F (175°C) and grease six ramekins or a muffin pan. Distribute the cake batter among the prepared molds, filling each halfway. Gently place one poached pear half in the center of each mold.

Transfer the molds to the oven and bake for 25-30 minutes until golden brown and spring back lightly when pressed. A toothpick inserted in the cake should come out clean.

Once baked, remove the cakes from the oven and cool in the molds for about 10 minutes. Run a knife around the edges to loosen them, then invert onto a serving plate.