1. Make the cake: Preheat oven to 325 degrees. Butter two 8-inch round cake pans. Line with parchment. Butter paper, and flour pans. Beat together butter and sugars with a mixer until light and fluffy, about 3 minutes. Beat in eggs, 1 at a time, beating well after each addition. Beat in vanilla. Whisk together flour and salt in a bowl. In another bowl, combine sour cream and baking soda. Gradually add flour mixture to butter mixture in 3 additions, alternating with sour cream mixture and starting and ending with flour mixture.

2. Divide batter between pans. Bake until golden and a toothpick inserted into centers comes out clean, about 50 minutes. Let cakes cool in pans, about 30 minutes. Invert cakes, remove pans and parchment, and let cool completely on a wire rack.

3. Make the filling: In a small saucepan, stir together 2 cups sugar, cream, and butter. Bring to a boil over medium-high heat, stirring constantly. Remove from heat.

4. Sprinkle remaining 1/2 cup sugar evenly in a shallow, heavy-bottomed, medium saucepan. Cook, stirring constantly, over medium heat until sugar is melted and light golden brown (sugar will clump).

5. Slowly add cream mixture to caramelized sugar, stirring constantly. Cook over medium heat, without stirring, until it reaches 238 degrees (soft-ball stage), about 10 minutes. Remove from heat and transfer to the bowl of an electric mixer. Let stand, without stirring, until temperature drops to 200 degrees, about 20 minutes.

6. Fit mixer with whisk attachment and whisk on high speed until thickened, about 6 minutes. Add vanilla and beat to combine. Let cool to room temperature, about 20 minutes. Divide filling into thirds. Working with one-third at a time, roll out on parchment paper into an 8-inch round; set aside. Repeat process with remaining filling.

7. Assemble the cake: Trim tops of cakes with a serrated knife to make level, then cut each cake in half horizontally. Place a bottom layer on a cake stand, and top with one round of filling. Repeat process with remaining cake layers and remaining 2 rounds of filling. Spread entire cake top and sides with caramel whipped cream, smoothing top and sides. Refrigerate cake until firm, about 30 minutes. Serve immediately or refrigerate up to 2 days; if refrigerated, let cake come to room temperature before serving.