Preheat the oven to 350 F. Line two 9" cake pans with parchment paper along the bottom. If needed, lightly grease the pans. Use non stick if possible. Set aside.If making homemade buttermilk: combine the milk and lemon juice, stir and allow the milk about 10 minutes to curdle.
Whisk together the flours, baking soda, baking powder, chai (or pumpkin) spice and salt. Set aside.
In stand mixer with whisk attachment or hand held with beaters, beat oil and room temperature butter on medium speed until smooth and well combined, about 3 minutes. On medium speed, beat in a slow stream of sugar. Beat until light, fluffy and well combined.This should take about 2-3 minutes in total.
Add eggs one at a time. Beat each egg for about 20 seconds before adding another egg. Add vanilla extract. Beat until well combined. Add caramelized apple puree a few tablespoons at a time. Beat until fully combined.
Using a large spatuala, mix the dry ingredients and buttermilk into the wet, in this order: dry, milk, dry, milk, dry. Make sure not to overmix.Wet cake strips if using and fit around the prepared cake pans. Evenly pour cake batter into each of the prepared cake pans. If using a food scale, make sure to take the weight of each cake pan prior to filling. Make sure the an even weight of batter is added to each pan. If you don't have a good scale, add 1 c to each pan until all the batter is added.
Bake at 350 F for 32-35 minutes. Cakes will be golden brown, with edges pulled slighly from the sides of the pan. The middle of the cake should quickly spring back when a finger is pressed gently onto the top, when the cake is baked through. If the indent slowly springs back, bake an addtional 2-3 minutes. Start checking for doneness around 30 minutes.
Once baked, rest cakes in the pan for 10-15 minutes on a cooling rack. Carefully invert the cake onto the cooling rack ( or plate placed on top.) Tap the pan a few times to encourage the cake to release. Lift the cake pan off the cake (which should be face down on the second cooling rack). Place the original cooling rack on the lined bottom of the cake. Gently flip right side up. Cool the cake on the cooling rack for about 1 hour.Wrap each of the cakes in plastic cling. Chill the room temperature cakes for 2-3 hours or overnight to make frosting easier. When ready to frost, pull the cakes from the freezer.