Preheat the oven to 350. Grease and flour two eight inch cake pans.
In a large bowl or the bowl of a stand mixer, beat together the sugar and butter until light and fluffy. Add the eggs one at a time, mixing well after each addition.
In a small bowl, whisk together the flour, baking powder, baking soda, and salt. In a small bowl or measuring cup, whisk together the buttermilk and vanilla.
With the mixer running on low speed, add the flour to the batter in three batches, alternating with the buttermilk. Mix until smooth. Divide the batter evenly between the prepared cake pans. Bake 30-35 minutes, until a toothpick inserted in the center comes out clean. Let cool completely.
While the cakes are baking, add the butter to a medium saucepan and melt over medium heat. Stir in the brown sugar, 1/4 cup of cream, and the salt. Continue cooking, stirring frequently, until the caramel mixture begins to bubble and simmer. Simmer two minutes, then remove from heat. Pour the caramel into a large bowl or the bowl of a stand mixer. Let cool for at least 30 minutes.
After the caramel has cooled, add 3 cups of powdered sugar and the remaining 1/4 cup of heavy cream, and mix until smooth. Add additional powdered sugar as needed to make a frosting that is smooth, with a buttercream consistency.
To assemble the cake, level the tops with a serrated knife. Spread 1 cup of frosting on top of one layer of the cake, then top with the remaining layer. Frost the sides and top of the cake. Drizzle with the caramel ice cream topping as desired, and serve.