Preheat oven to 350℉. Butter and flour three 9-inch round cake pans. Line the bottoms of the pans with parchment paper as well. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, allspice, cloves, and cardamom. Set aside.

In a large bowl, whisk together the eggs, brown sugar, granulated sugar, vanilla, vegetable oil, and buttermilk until smooth. Fold in the grated pears. Add the flour mixture and stir until combined. Divide the batter among prepared pans and smooth out the tops with a rubber spatula. Bake for 22-24 minutes, or until a toothpick inserted into the cake comes out clean. Cool cakes in pans for 20 minutes, then cool for the rest of the way on a wire cooling rack.

In a medium saucepan, bring the sugar and water to a boil over high heat. Cook until the sugar is dissolved, but DO NOT stir! Swirl the pan on the stove if you need to. Continue cooking, without stirring, until an amber caramel forms, about 6-7 minutes. Remove from the heat and carefully stir in the cream, and continue to stir until smooth. Add the butter, vanilla, spices, and salt, and stir until combined and the butter is melted. Let cool.

Add the apple cider, water, and star anise pods to a medium to large saucepan. Bring to a boil and add the poached pears. Reduce heat slightly and simmer for 20 minutes, or until pears are tender.

Melt the butter in a saucepan over medium heat. Once it has melted, start whisking constantly. Watch carefully, it can burn easily if you don’t keep an eye on it! The butter will start to bubble and get a little foamy, and develop a golden brown color with a nutty aroma. This can take several minutes, just keep whisking and make sure it doesn’t burn. Once you see the brown bits start to appear, keep cooking for a minute or so until the butter is browned. Remove from heat and transfer to a bowl. Place bowl in the freezer to firm back up to room temperature butter. This can take 20 minutes or so. If it gets too firm, place it in the microwave for a few seconds to soften it back up.

Add softened browned butter to a stand mixer fitted with the paddle attachment and beat for 2-3 minutes on medium to medium-high speed or until light and fluffy. Lower the speed and gradually add the powdered sugar. Once powdered sugar has been incorporated, add the vanilla, heavy cream, and salt and increase speed to medium-high. Beat for an additional 2 to 3 minutes until light and fluffy.

To assemble the cake, place one layer on a serving plate or cake stand, and spread the top with buttercream. Top with another layer and spread top with buttercream. Top with the third layer and spread with another layer of buttercream, leaving a little bit left for the sides of the cake. Use the leftover buttercream to "half" frost the sides, to create a "semi-naked" effect. Use an offset spatula or bench scraper to smooth out the sides of the cake. Pour the chai caramel over the cake and let it drip down the sides (you might not use it all, just use your desired amount!). Top the cake with the poached pears. Slice and serve!