For the cinnamon spice cake: Preheat the oven to 350 degrees F. Line two 9-inch cake pans with parchment paper and lightly butter.
In the bowl of a stand mixer, beat the butter, shortening, brown sugar and granulated sugar together until smooth. Beat in the eggs 1 at a time until smooth and light. Stir together the buttermilk and vanilla in a separate small bowl. Sift together the flour, cinnamon, baking powder, baking soda, nutmeg and allspice in a large bowl. Alternately add the flour mixture and buttermilk mixture in thirds to the mixer bowl, blending well after each addition.
Pour the batter into the prepared pans and bake until a cake tester inserted in the center of the cakes comes out clean, about 35 minutes. Cool about 5 minutes, then turn out onto a cooling rack to cool completely, about 10 minutes.
For the fig buttercream: In a clean bowl of a stand mixer, cream the butter until smooth. Add the confectioners' sugar and beat until incorporated. Mix in the fig butter. Add the buttermilk if needed to thin to a spreading consistency.
For the buttermilk caramel: Combine the granulated sugar, buttermilk, butter, corn syrup and baking soda in a LARGE pot. Do not use a saucepan; it may boil over. Bring the ingredients to a boil and reduce the heat to low but still bubbling. Cook, stirring very frequently, until golden brown, 8 to 9 minutes. Remove from the heat and add the vanilla. Let cool.
For the white chocolate ganache: Put the white chocolate in a heatproof bowl. Heat the cream in a saucepan until just simmering. Pour the cream over the chocolate and let stand for 5 minutes. Stir until smooth and melted. Refrigerate until cooled completely, about 20 minutes. Transfer the ganache to a clean bowl of a stand mixer fitted with the whisk attachment and whip until smooth.
To assemble the cake: Slice each cake layer in half horizontally. Place a layer on a plate or cake stand and cover with fig buttercream. Repeat with 2 more layers and the buttercream. Put the final cake layer on top, then frost the top and sides with the white chocolate ganache. Pour the buttermilk caramel over the top of the cake to drizzle down. Serve with more caramel sauce if desired.