Special equipment: a pastry bag fitted with a large open star tip (such as #362)
For the cake: Preheat the oven to 350 degrees F. Spray three 8-inch round cake pans with cooking spray.
Place the brown sugar, granulated sugar and butter in a large bowl; beat with a mixer at medium speed until well blended, 3 to 5 minutes.
Turn the mixer to low and add the eggs, 1 at a time, beating well after each addition. Beat in the pumpkin and vanilla.
Combine the flour, cinnamon, baking powder, baking soda and salt in a bowl, stirring well with a whisk.
Add the flour mixture and buttermilk alternately to the sugar mixture, beginning and ending with the flour mixture. Spoon the batter into the prepared pans.
Bake until a wooden pick inserted in the centers comes out clean, 22 to 25 minutes. Cool in the pans on a wire rack for 10 minutes, then remove from the pans and cool completely on the wire rack, about 1 hour.
For the cinnamon buttercream: In a large bowl or stand mixer fitted with the whisk attachment, whip the butter on medium-high speed until pale and creamy, 3 to 5 minutes. With the mixer on a slow speed, carefully add the confectioners' sugar 1 cup at a time until combined, followed by the vanilla and cinnamon. Add the heavy cream a little at a time. (If you need a thicker frosting, add more confectioners' sugar; if you need a thinner consistency, add in more heavy cream.)
Place a cooled cake layer on a cake stand. (This recipe should yield very level cake layers, but if your layers are domed, level them before assembling.) Cover with about 1/2 cup buttercream. Scatter 1/3 cup of chopped pecan over the top.
Repeat with the next layer of cake, covering with 1/2 cup buttercream and 1/3 cup chopped pecans. Place the final layer of cake on top.
Place the remaining buttercream in a pastry bag fitted with a large open star tip (such as #362). Pipe out a design on the top of the cake (the sides will be left "naked").
Sprinkle the remaining pecans over the top, then drizzle the cake with caramel sauce. Serve immediately.