Heat oven to 350° F.
Start your cake batter by preparing your cardamom. Open the pods and remove the seeds. Then, grind seeds in a spice mill or with a mortar and pestle.
Next, place flour, sugar, cold butter, baking soda, baking powder, salt, and ground cardamom into a large bowl or mixer.
Mix dry ingredients plus butter on a slow speed with the paddle attachment until the butter is fully cut into the dry ingredients and forms a loose sand-like texture.
Peel ripe pears and remove the core. Place the ripe pear flesh into a medium bowl and mash with a fork.
Add milk, eggs, and vanilla to the smashed pear and mix together.
Then slowly add the mixed wet ingredients to the dry ingredients while mixing at a low speed. Once the wet ingredients are added, increase the mixer to medium speed for 10-15 seconds until the batter is well combined.
In a 12 inch cast iron skillet, melt butter on medium heat.
Once the butter melts, add brown sugar and stir in until the butter and brown sugar are combined and just starting to simmer. The caramel mixture should coat the bottom of the pan.
Turn off the heat and lay thinly sliced pears around the pan in a circular pattern.
Spoon cake batter into the skillet and use a spatula to spread the batter to the outer edges.
Bake cake in a preheated oven for 20-25 minutes. Check for doneness by inserting a toothpick into the cake. The toothpick should come away from the cake clean.
Remove the baked cake from the oven and let rest for 5 minutes in the pan.
Run a knife around the edges of the cake pan to make sure the cake is loose before turning.
Then invert the by resting cake plate by resting the cake plate on top of the skillet and carefully flipping the skillet and cake plate together to turn your upside-down Cake right-side up to reveal the caramel and pear design on the top of the cake.
Serve alone or with a scoop of vanilla ice cream for a delicious winter dessert.