For the Pears:
In a pot, bring cider, cinnamon, cardamom, and 1 cup water to a simmer.
Add pears and cook while stirring for 20 minutes.
Remove pears from the liquid and dry them on paper towels, then cool completely.
For the cake:
Preheat your oven to 350.
Grease a 9" cake pan with nonstick spray, and dust it with flour the line it with parchment paper.
In a bowl, whisk together coconut oil and brown sugar.
Add the egg, vanilla, and buttermilk, and mix.
Add almond flour, 3/4 cup all-purpose flour, baking powder, baking soda, salt, cinnamon, and cardamom, then mix.
Toss pears with 3 tablespoons flour to coat.
Pour 1/4 of the batter into the pan and tightly pack pears into the pan on the batter.
Pour the remaining batter into the pan and tap to remove air pockets.
Bake the cake until a butter knife inserted into the cake comes out clean for 50 to 55 minutes.
Cool in pan for 20 minutes, then flip over onto a plate to cool completely.
Carefully remove the parchment paper, and if a pear slice becomes stuck slide it off with a spatula and place it back onto the cake.
Sprinkle the cake top with powdered sugar before serving. Enjoy!