Cut the base of the cake into two slices. Place one piece on a cake platter and place the clean ring of the springform (or a special ring for this kind of purpose) around the cake slice.
Assemble cake: Pour ½ of the buttermilk-whipping cream mixture on top, level with a spoon, and cover with the second cake slice. Pour the rest of the buttermilk mixture on top, level nicely.
Let set: Place the cake in the fridge until set, ideally overnight.
Release cake: When the cake is set, carefully go around between the cake and the springform ring with a knife. Remove the ring carefully.
Cream: Whisk the rest of the whipping cream slowly adding the stabilizer, if using any. Place a few tablespoons of the cream into a piping bag with a nice nozzle of choice. Spread the rest of the whipping cream on top and around the edge of the cake.
Decorate the cake with whipping cream from the piping bag, pistachios, and lemon slices.
Refrigerate until ready to serve.